I have just summarised a video by Psychiatrist Alok Kanija for myself, which is about maximising the benefits of empathy and lowering the drawbacks. It generally pleads the case, that people are getting more selfish and naricicistic, but the rarer empathy becomes the bigger the benefits become, sort of in a market supply/demand function.

In order to actually practise empathy well and dampen yourself of the negative sideeffect you need to:

1. Leave the stress with them after helping them
Mentally seperate the action of helping and your own life, you are not them

2. Help them help themselves, instead of solving their problem
A bit of a video gamey metaphor, but they need the experience they get from completing the skill check of fixing their life, in order to fix future issues. You are not supposed to roll the check for them, just give them a buff on the roll.

3. Be able to step out of your own perspective
The more closely you can render other people in your head and visualise their perspective, the more effective your help will become, and somewhat surprisingly, the less you will be emotionally affected by them

4. Be able to lower your own stress yoursef
Even with all these techniques, helping others is stressfull. You need to be good at standard coping mechanisms, journaling, walks in nature, video games, meditation, whatever works best for you.

5. Actually want to help them
He cites some fascinating research, that the motive has massive outcomes on the effect of helping others on yourself! You only reap the neurobiological rewards of empathy (higher dopamine/serotonin etc), if you are primarily motivated by actually bettering their life, not by being interested in return rewards, or even in those very biological rewards you get for helping others.