Hi, my son is transgender and I'm a parent but can help with this, I think. We lived in Summerfield, Fl. This is a place between Orlando and Ocala. Fl is by far one of the worst places I can think of to live as a transgender person. Our family gave up all our resources to get my son out of there. Orlando is a decent place and Miami is really a wonderful place too but very expensive. Gainesville is part of the 'country' areas in Fl and are very closed. Not to say the whole city is bad and we didn't have as many problems as where we lived (a true nightmare-right down to the very southern police). There are some very hip parts of Gainesville as there is a college but not enough to give you a happy life with the resources you are used to in Seattle. We travelled to Jacksonville (a 3 hour drive) monthly to get my son's therapy and were lucky to find this. We did find someone in Orlando but I was appalled at not only the cost but the misusage of correct pronouns, etc that the staff at this place used. When I spoke up about it, the response was that this was a place all the transgender youth came to and they were backed up with appts. I believe it. I could go on but I will tell you our family gave up all financial security to get out of there. Employment, our home, you name it. We went as far as possible and are now in NY. It was a little frightening but it was much, much better then the choice to go on in FL. My son is much, much happier and so are we with watching the many more choices he has here. It's still frustrating for some things but there are different options to get over the little frustrations in comparison. I also would really be concerned about the relative you are staying with. Many times people are supportive of relatives and try to help but in the end, are not equipped to deal with the challenges transgender youth face. It can become a frustration for everyone and won't help you. I would really be concerned that you will face a life you don't like. Coming from the north to the south is a sort of adjustment for anyone but for those whom can face ramifications of ignorance, it is really a difficult life.
I know it's not as simple to find a way financially to stay there in Seattle, believe me. It can be a very difficult thing but please weigh the options you can have very carefully. Seattle was a sort of dream place for us to go when trying to leave Fl but was quite expensive for our entire family. My husband and I have responsibilities for our children and more then just one person. We even looked to go down to mobile homes and use the rest for stability until we could get a job or something. We were that desperate to get our son out of FL. Even if you can get a job working something you can hate right now, your future years ride on this decision.
I truly wish you the best of everything.