You're 21? So why not move out? If your situation doesn't allow it I understand, but either way, you're an adult and they can't make you do something like that.
Your mom is afraid for you, they all are at first. It's likely she can't envision your future being better if you transition. I'm going to assume she knows very little about the condition at all. Everyone's afraid of the unknown. You are in the know. Take the time to educate her. Show her the science behind transsexualism. Give her examples of trans guys who have successful lives and are in happy relationships--this is a big deal to parents. They might think you will never be accepted by anyone, which is blatantly untrue. They just want to be sure, and for you to be sure, that this is the best possible decision, not just now, but for the rest of your life.
It's not a hormone imbalance that's causing you to feel the way you do. I guess you could prove that by getting your T and E levels checked, but there's no reason to do that just to appease someone else. Many trans guys have normal hormone levels by female standards before transitioning. Granted, there might be just as many who naturally had higher T levels, but these variations are present in every person, male or female or anything in between. Cis females with PCOS still identify as female, despite having high T.
Anyway... Just talk to her. Have an honest open discussion. Sometimes you have to be the educator.
PS: If you're at a loss as to how to introduce this to your parents, try showing them any skylarkeleven video on youtube. I've used his videos to explain things to family and I chose him because, really there's just no way that anyone could look at him and say he's made the wrong decision. He's simply a beautiful person and you can see that just from watching ten seconds of a video.
