My ds13 was diagnosed with depression around age 8, (due to social issues mainly) and anxiety (due to social issues/feelings of not fitting in/school ) and was very sensitive to meds *always*. Although not adhd /on meds for that, when given asthma meds he would break down in tears over things that just weren't a big deal.
I've even had this effect myself on allergy meds. It's just awful. I avoid those altogether for him/me or take very very small doses if absolutely necessary. We work with a good allergy/asthma doc to keep an eye on things.

In any event, as school didn't seem to be bringing him any social benefit and seemed to be the touchpoint for most of his issues, eventually we looked towards removing him from the school and homeschooling and after a couple years he is really really a joyful kid all the time. It is a huge relief.
We did find a social skills course at the time, mainly I think it helped ds see that he really was just somewhere on a continuum of 'normal'. Also the anxiety coaching was helpful; laying out for him some things to do when he would start to worry about stuff: make a list of what you're worried about.
Within reason, can you do anything about the worry? then make a plan to deal with it and follow through. Also talk about it with adults.
If you can't do anything about it, then realize this and try to get ok with the fact that worrying about it would not help anything.

Best of luck with your ds!