Late to this thread but my 2 cents: if you really have the problems you think you do then they are likely to get worse in college. Assuming your goal is to complete college, then your mental health issues sound like your single largest obstacle to success. Your parents are going to know in the end anyway. I assume they are paying for your school and/or insurance. They have a right to know what they are paying for even if you have a right to restrict the nitty gritty of the details.
Were it me, I would start at the school counseling center for a free assessment and tell them your concerns. If they are unconcerned, then your problems are solved. If they tell you that you have relatively minor issues that are solvable within the confines of short term (< 12 free session) therapy, then problem solved. If they diagnose a significant condition that requires psychiatric evaluation and treatment, then you should tell your parents. Like it or not, you need them and whether they like it or not they need to be decent.
If you truly have something like bipolar disorder that has potentially significant consequences, then you should get established with a psychiatrist and therapist privately outside of the college system and payed for with your parents’ insurance.