Is it worth it to go out of state just to transition?

Hi, I live in a state that provides free tuition for any schools in-state because of an academic program I am in. However, I am transgender and I live in a rural area in the south. I really feel like if I live here into my adult life I will see no progress within my transition, and to be honest that is more important to me than education at the moment. My plan is to move out of state to pursue my transition, whether if that's through going to an out of state college or after I graduate college here. But going to an out of state college would let me begin transitioning faster.

I would also like to note that my family is very much willing to pay for a portion of college, and I have a G.I. bill from my dad that I can use for housing. I just don't want to be too much of a financial burden to them, when college is free in state.

Essentially what I'm asking is: Is it better to stay in state, get basically free college, but not be able to transition until I move out of state, or should I prioritize my happiness and attend college in a much more liberal area, but spend more money?