I don't think you're being too sensitive, and your mother sounds INsensitive and somewhat manipulative.
But let me just explore this a little. You say you aren't out to her yet, so I'm wondering how she is supposed to even get a chance to understand. On the other hand, you say that you've tried to explain why you have anxiety about leaving the house, but she doesn't listen...does that mean you've tried to come out to her? Or have you tried to uh, skirt the issue (sorry, couldn't resist) and put things into a non-trans context? If the latter, your reasons for anxiety could come across as trivial and silly because she doesn't have the trans context she needs. Then again, it sounds like she wouldn't listen no matter what, but I have no way of knowing.
I'm probably the last person in the world who would feel sympathetic toward anyone's mother, but I have to wonder if your not being out puts you BOTH in a double bind. I completely understand that you have reasons for not coming out to her, but does the landscape shift a little when you try to see it from her perspective? Or am I just cutting her way too much slack here?
Anyway, I like the idea of throwing the "I didn't mean to make you feel bad, but you're too sensitive" back in her face. If you don't mind coming across as a little obnoxious, and if you don't think the repercussions will be a problem, give that a try. I wonder what she would say if you responded with, "Gee, you think I'm too sensitive, and yet you keep saying things that are obviously hurtful. From this I conclude that either you take a long time to learn the obvious, or you go out of your way to hurt others. Which is it?"
Doubtless she would back and fill, and try to put it all on you. People will tell you that someone else can't make you feel bad without your permission, but I think it's a bit more complicated than that. When people figure out what buttons to push, and when they enjoy pushing those buttons, there's something seriously wrong with THEM. But if you can find a way to not care what others say--that is, take away the buttons--you'll probably be happier in the long run. Easier said than done--there can be a steep learning curve for this. Like, years. Which does you no good now (I didn't have that skill at your age--far from it). But keep working at it for the future.
It looks like you live with your mother. If so, I hope you can find a terrific job (no skirts or dresses) that enables you to move out so you can live your life on your own terms. That ought to dull her fangs a little.