Are you sure that the correlation between immune health during childhood and all of those positive attributes is causal?
Superficially, it seems more plausible that the causation starts much earlier, via mutational load or specific conditions during the gestation period. Though I suppose that it is also possible that health in the womb and health during early childhood could both effect adult outcomes.
Maybe I'm missing something, but I think you miss the most obvious way to improve your social skills: practice! Receiving positive social feedback is a skill and like all skills can be improved.
While there is a wide distribution in natural social competence, a large portion of the variance in social skills is attributable to how much time you spent interacting with other people during your formative years. The more time you spend with people, the less you have to think in social situations. You will have the experience to know what are the typical things to do and say, how people tend to react in certain situations, how to read various subtle micro facial expressions and shifts in body language, etc.
Of course, if you are in actively toxic environments, then I would not recommend recklessly "putting yourself out there". If you are still shy or lacking in confidence in your social skills, it is wise to limit yourself to social settings that you are comfortable, at least in the beginning.