If you like and love design, coding and critical thinking - then yes go for SW Engineer. That could be ideal main stream as career. As not many in the class have these niche skills. So go for it and prepare yourself for engineering.
However, that wont kill your other dream:
As you love solving others problems and must be a good advisor too - you can still continue to practice it in parallel, ready books, youtube video, attend sessions/seminars and take up a part-time program/study on psychology, get certified as well.
And always remember on a lighter note - You will always have a chance to help your SW Engineer co-workers with your Psychiatry expertise but you can't treat Psychiatric patients with SW Codings :-)
So why choose one, when you can be both?
Good luck and long pleasant way to go..