I don't see why it would stop you as long as you feel ready and well enough to complete the coursework and placements. The uni isn't going to look into your medical records, all they need to know is if you have any current physical or mental health issues that they would need to provide support with during your time with them. You don't have to disclose anything that you don't want to when it comes to your medical history. Occupational health will ask the same questions and will also ask for proof of vaccinations. When you get referred to Occupational Health, it is worth mentioning your history with mental health services just so you have some support if you need it.
Lived experience of mental health issues can be very valuable as a mental health nurse but I do agree with the other commenter, keep it to a minimum at your interview. Just telling them that your lived experience inspired you to want to be on the course would be enough.
There should be plenty of support at your uni to help you out once you get on to the course.