This is something I would love to collect more data on. Everything here is anecdotal and speculative.

The first pill I tried was Sprintec, a combination estradiol and norgestimate, and it caused at least 3x/week panic attacks for the entire 5 months I was on it. I would say do not recommend, but with any birth control YMMV.

Now I am taking Larissia, which is a small-dose estradiol and levonorgestrel combination. I think it has made me slightly more depressive (with slightly decreased productivity as a consequence), but it is FAR preferable to Sprintec and marginally preferable to no-pill.

Off the pill, I find my productivity above-average for about 1 week after my period (I have a very regular 28 day cycle), and frustratingly low for the other 3 weeks (especially the week I am actually on my period). While on the pill, I never get the high of that one post-period week, but I also don't suffer the low before and during my period.

The reason I start Larissia is because I took a levonorgestrel emergency contraception (specifically Aftera), and I was expecting to spend the next few hours bedridden with nausea, but I actually found my mood lightened and my productivity increased, roughly to the level of my non-pill post-period high. Of course, this was just one time, and the Aftera tablet is 1.5 mg of hormone where Larissia is .02 mg. I'm considering switching to the slightly higher .05 mg levo-estra combination to see if I can alleviate some of my current depressiveness.

Hope this is helpful! Definitely a question I've wondered myself, and it's good to know I'm not the only one.

I think your symptoms are substantially worse than average. I've only spoken to or heard of one other person with symptoms that bad -- Julia Wise, actually, who has written about it on her blog. https://thewholesky.wordpress.com/2016/12/23/you-dont-need-to-have-a-period/

Mine are also probably worse than average, but not as bad as you describe. I'm usually unable to work or do much other than read or some other low-key activity because of pain, for about half a day to a full day at a time. I've never experienced vomiting due to pain.

I got an IUD ~7 years ago that basically made the problem go away completely. I've had a couple instances of extremely severe pain with the IUD that were so bad I went to the ER, but since it mostly deleted my menstrual cycle and there were only a few bad days in many years, I feel it was a good deal on net.

I would +1 all the commenters here saying you should investigate more birth control options that could mitigate the severity -- and probably try to find better doctors, if you can. I think it's a common experience for period pain to be dismissed as unimportant or not worth spending effort to fix, but that's utter bullshit.

I've gotten a lot of mental mileage out of thinking of it as "This is a minor physical disability that I have," and try to think how I would want to work around it if it were a Real DisabilityTM. For example, I used to feel guilt about taking time off work because I was in so much pain that I couldn't concentrate, because "periods are normal, if I can't work during this normal thing, then that means I'm a bad employee." Instead, I changed my thinking around it to be more like "This is a disability I have, and so my employer can accommodate it. If it's a problem for them that I have to take off half a day here and there, we can discuss it and negotiate it, but I'm not actually able to work right now, so there's no point staying here and pretending."

Probably obvious, but have you talked to a doctor about this? Or several doctors? That sounds terrible.

I don’t have menstruation-related symptoms severe enough to affect productivity. I also don’t use hormonal birth control.

My cycle:

First one-two days of period:
A lot of pain, occasionally it makes me vomit, it always makes me unable to do anything
Lots of physical symptoms such as diarrhoea
Super tired (from the pain?) and need to sleep for half the day
I think extremely slowly during this time
I think the best description of this state is that I’m ill

Last two-three days of period:
Quite neutral state of being

First two weeks after period:
Mentally calm
More able to concentrate
This is the best time for boring but important work

Third and fourth week after period:
[These effects slowly get more and peak in the second week]
Emotionally more fluctuating, more ecstatic, more crying, more anger, higher libido
Cognitively I’m sharpest during this time (I can think the fastest but can’t focus that well)
This time probably comes closest to mania for me

I have two data points for dealing with this successfully, and both amount to "make it stop" instead of "improve things":

• One of my sisters "doesn't have time for this crap" and one day just stopped taking the placebo pills from her normal birth control and stayed on the active hormones continuously.  This apparently suppressed her period.  After doing this for about ten years, she stopped and successfully conceived at almost 40 years old.  This is not medical advice, do your own research, etc blah blah.
• One of my female friends has had an IUD for ~15 years now, which over time reduced her period to occasional light spotting and dramatically reduced general symptoms and inconvenience.  The startup period (first year) was rough though, as was the first six months after the first replacement five years in.  The second replacement was basically not a problem.

It should be noted that I'm aware of multiple attempts to use IUDs within friends and family, but only have one data point that was long term successful.  Apparently the first year of an IUD can be brutal and it's not uncommon to give up after a few months.

Pain control:

I’ve tried taking paracetamol during my period, but it doesn’t affect the pain at all.
I now use feminax (have been using it for a couple of years), and it does reduce the pain, but no other symptoms, e.g. I still need to sleep a lot and still feel ill.
To mitigate the pain I also take a lot of hot baths and use hot water bottles

Pain as a symptom:

I’ve never gotten myself tested for endometriosis, but it doesn’t seem unlikely to me that that’s what causes the severe pain. The main symptom for endometriosis is painful periods. One in ten women are suspected to have it, but it’s very underdiagnosed. Maybe that’s because GP’s don’t take the pain seriously? I asked my GP about pain control and he suggested I go on the pill, and did not even mention endometriosis.

I don't menstruate, but I work at Natural Cycles (a data-driven birth control app) with data science, and look for these types of patterns a lot — our users are not using Hormonal Birth Control though, so the sample is biased in that way. 

Clue (a popular period tracker app) recently released one of the best studies I've seen on the mood changes over the menstrual cycle, but unfortunately it is not open access. The authors shared a pdf with me after I emailed them though, DM me if you would like a copy (sci-hub doesn't seem to have the paper yet), or email the authors directly, they are very helpful. 

I have suspected there might be mood/energy effects but never managed to track my cycle and mood well enough to show a correlation. It's only gotten harder to track since my IUD lightened the bleeding to almost non-existent.

I don't menstruate but my ex-wife did have effects like you describe and took a while to find a working medication regime. I have some notes about the effects of the menstrual cycle in my Anki deck. It is not super relevant to your question but might be relevant to the menstrual cycle in general.

The menstrual cycle can cause the following potential symptoms (note that of course, I do not think that these happen always or in noticeable strength but the list helped me relate to the often unspecified effects):

Physical

• Abdominal bloating 
• Leg cramps
• Temporary hypoglycemia
• Headache
• Acne
• Constipation
• Oedema
• Breast swelling
• Weight gain

Emotional

• Depression
• Anxiety
• Anger
• Guilt
• Mood changes
• Panic
• Low self-esteem
• Fatigue
• Aggressiveness
• Psychosis

Behavioural

• Intolerance
• Intense Irritability
• Restlessness
• Social isolation
• Sugar and salt craving
• Insomnia
• Increased use of alcohol
• Hysteria
• Confusion
• Physical Violence
• Accident-prone
• Anorexia or Bulimia
• Libido changes
• Suicidal
• Lack of self-control

Unfortunately, I couldn't find the original source but you can find these symptoms listed e.g. here.

I was also about to mention that the cramps may get better after pregnancy as I knew from anecdotal evidence but then I had a look and it can go either way (though there is a relieving effect in severe cases).