My mom wants me to move to fl with her and I have a pitbull an I'm wondering if they are allowed there, if not my mom can go by herself.

Here are 2 articles for you to look at. Niether of them confirm or deny pitbull banning. They just talk about upcoming legislation. It may not have passed at this time but can pass after you move. So you may be affected by it.

Ref:

Pit Bull ban possible in Florida | Tampa Bay, St. Petersburg, Clearwater, Sarasota | WTSP.com 10 Connects

Owning a pit bull could soon be illegal

You should call the MLA in the county that you are moving to and find out. Also make sure to call around to a few insurance agencies to make sure they will insure you with you breed.

This is a link to the Tampa municodes. It is a place to begin. You will also want to check state and county regulations.

Municode - Search

Landlords, insurance, etc. are other places that might have restrictions on breeds that are allowed by them.

Tampa government website for more information you and your mother might need to know before relocating:
Citizens Guide