I live in Florida too. And I know for a fact, the people aren't always the most accepting. It really depends on where you live and other factors. However, no matter what career you look for, as the person above me has stated, you WILL have to go through some sort of background check most of the time. And it's not like you're pushing drugs into your body without a medical reason or without permission from a doctor. You aren't doing anything illegal. So before you take any drug test, you should explain that. And let's say you don't work for the government as a social worker, other jobs too require drug testing.
There is no way that EVERYONE would refuse to hire you because you're trans. If it really worries you, try applying in areas where you know people will be more accepting/tolerant. I hear that Ft. Lauderdale, Tampa, Orlando, and I believe Key West are great areas for the LGBT community. Think about it this way, if they don't hire you because of who you are, then maybe you never wanted to work for them in the first place. They did you a favor.
I'm getting my degree in Criminal Justice. I considered Social Work as well but for various reasons I have decided to just stick to CJ. I'm hoping to get a job in probation/parole which is pretty much social work but for criminals. Don't let being trans get in the way of your dreams. If you do, you are letting the ignorant win. Be proud of who you are.

Oh and on a side note, how did Florida laws change? I haven't started T yet but you said something about that. If you could explain what happened I'd really appreciate it