Hello, and WELCOME to Allnurses.com
Not knowing you or your individual situation, I'd have to say that a lot depends on whether you take medications for your conditions, if you're seeing a psychiatrist or psychotherapist regularly, and how strong your drive is to become a nurse. This is not a career for the faint of heart---you must understand that stress is a constant companion not only in nursing school, but out in the working world.
That said, there are a great
many nurses with psychiatric illnesses who are successful in their jobs; for example, I have anxiety and am diagnosed with bipolar disorder, but I've reached management level (DON in an assisted living facility) and am reasonably good at it. A friend I went to nursing school with who has ADHD works as an assistant director in the Behavioral Health unit at a 400+ bed Magnet hospital. And I'd be shocked if there weren't at least as many nurses with depression as without it!
Whatever a nurse's health issues, most will thrive if they can find their 'niche'---the right area of the profession for them. Do some research, look around at the different specialties and see what might appeal to you. Generally, you'd want to avoid jobs where it's super fast-paced and the adrenaline flows freely, like the ER or critical care; on the other hand, a paperwork job might bore you to death with the lack
of adrenaline, so you have to weigh your options carefully.
Good luck to you!