What stands out to me is the *4 years* you have not had your period. You had to be seeing doctors because you did have some illness. Doctors almost always - if not always - ask when your last period started. I think that they do that (when you are in a child-bearing age range) to have some insight into what they are seeing. Don't know, but it IS a standard question.
So, gynecologist aside (pap smear time, a gyno for certain asks about periods), at least one of these doctors might have hazarded a guess. They know medications, they know cycles, they know bodies! Maybe they don't know answers but they know where and how to look. So, for sure your family physician will have an opinion or send you to someone who has a better-informed opinion.
Good luck! You take good care of your health with diet and exercise (your BMI is in the normal range) so that's a huge plus.