Menopause doesn't usually start this early in life unless there is something else going on that needs to be checked into. If I had a doc who wanted to put me on the pill to "fix" my period problems, I'd fly out the door fast. And BTW, going on the pill will often screw up chances for fertility even more, although I know you wisely declined this option.
Did you have a pelvic exam to rule out whether you may have cysts? I would look for another doc who would give me an ultrasound and other tests to see if there is anything that is interfering with my normal ovulation cycles and take it from there.
You may also want to have your thyroid tested, as this can also play havoc with your reproductive system.
Once you know what's causing the irregularity, it's much easaier to find the least invasive treatment.
Blessings to you.