The Synthroid is not going to hurt you, especially at 25mcg (it's in micrograms, not milligrams). Take it now and make sure they wait at least two months before they do a follow-up blood test. It takes at least that long for your body to adjust to the dosage. If it turns out that you don't need the Synthroid, a few months of it won't hurt you. Yes, the majority of people with hypothyroidism are older, but younger people have it, too.
Your irregular periods and excessive tiredness could definitely point to hypothyroidism. Once you've been on the medication for a little while, you probably will start to feel better. There are only three basic thyroid level tests they do, and they mostly just do TSH, which is like your body's request for thyroid hormone. If the number is high, it means you aren't getting enough. If it's too low, you are getting too much.
For such a minor issue, I don't know if it's necessary to see an endocrinologist, especially if you don't know if your other doctor is able to treat it effectively or not. But it is totally your choice. Just make sure you don't have too many cooks in your thyroid kitchen--find one doctor (that you can see on a regular basis) and stick with them when it comes to your thyroid. Don't have multiple doctors managing it.
May I ask: what are you really worried about? Why are you so resistant to taking the Synthroid?
