Nami’s family to family class would be excellent for your parents. Unfortunately there probably isn’t a lot they can do other than be supportive and be present to step in to keep you from doin any serious harm if you begin to get badly depressed or manic. If you know what your warning signs for either of these are and you are trusting enough of your parents, the best way they can probably help you is to be willing to step in and take control when necessary. E.g. If you are a wild spender when manic, have an agreement that they will take your credit cards when they see signs x, y, and z.
As both the spouse and the parent of people with serious mental illness, I can assure you that your parents do not want you to worry about lessening the burden on them. They would gladly shoulder any burden if it would make you well. Unfortunately getting mental illness into remission (because that is really what we are talking about, not recovery or cure) can be a slow, frustrating, trial and error process. If you have tried several medications or medication combinations without success, I always encourage people to seek out a psychiatrist who specializes in psychopharmacology. You may have to go to an academic medical center to find someone like this, but the difference is amazing as they really can break down the specific elements of your symptoms and select medication based on that in a way I have never seen another dr do. Also keep in mind that the best medicine for you may be a “cocktail” of several different meds. There is nothing wrong with that. Whatever keeps you feeling well and functioning at your best is appropriate. I know several people in high-level positions who take long lists of psychotropic medications.
Secondly, you need to find a counselor who will help you with some coping skills. Often people with mood disorders have not been able to learn ordinary coping skills because you have just been trying to survive. Medication will get you to the point where you are able to exercise coping skills, but you are going to be behind your peers in terms of learning them, but a good therapist will get you there. The younger you are when you start this the better (having observed a teenager and a 40 year old both going through the process at roughly the same time).
I wish you all the best. You have taken the most important first steps by recognizing your illness and seeking help.