I recently went to DMV in CA and found out that I cannot get a drivers license until I pay a fine I owe from a driving on suspended that is about $800 now. I am planning on leaving for Texas this next week and was wondering if I would be able to get a Texas drivers license while I am down there or if the fine from CA would show up down there, too..

It will show up,

DMV's have a habit of running your information and getting the skinny on you from all the other states. You need to pay that $800 fine or you won't have a DL at all, in any state.