Hey, the mentally ill can study psychology! You will be wonderful, really. If it's something you want, I'd say go for it.

As for science, I know it can be terrifying. I first went into college (or uni, which ever you prefer) as an art major. I ended up as a bio major minoring in abnormal psych. I was TERRIFIED to get into biology, chemistry, physics, because despite my abilities to do well with scientific practices and understanding theories, I am a horrid math student. I am learning disabled, and that took a huge toll on my self confidence when it comes to education. My choice was to give it a try, find math classes related to the sciences, and with a lot of help, I managed to do well.

Definitely talk to some professors and ask about restrictions, etc. It's better to know the limits beforehand, I think.