I live in England. I used to be a social worker and one of my various jobs was supporting people at my former university who had a psychiatric diagnosis, including Americans on the School's study abroad course. My experience was that it was very, very difficult for them to get reciprocal treatment on the National Health Service. Referrals will often take up to six months, and it was not uncommon for an American to see an English psych once time and have their diagnosis and meds from the US completely changed. Quite a few drugs you have licensed over there are not available here, too.
ETA: And provision of talk therapy is mostly dependant on either having enough money to pay for it outright or on being sufficiently linked with a local borough to get on their NHS therapy waiting list and then waiting for months and months. Some unis do have counsellors you could see, though.

So that's not a small concern. I'm not trying to scare you off, but yeah. It's a serious consideration. The ethics and philosophy (as well as availability) of psych treatments and medications are different around the world. It's something you should research very carefully if continuing your med regime is important when you go abroad.