I've lived in Colorado for the last four years but was born in Harris County in Texas, which is where my birth certificate is issued from. I'm trying to start the process to change my legal name and gender. I'm looking to change pretty much everything, but I don't have a driver's license and I'm aware that changing a birth certificate in Texas is pretty difficult to do. The problem I've run into is that Texas law states that you have to file in the county you live in, but I haven't lived in Texas in years, so I have no idea where I'm supposed to start now. Can I just change everything except my birth certificate here in Colorado and then worry about that after everything else is changed?

Yes you can and (need to) change name where you legally reside currently. The birth certificate matter is another can of worms involving the Texas court system. While a certified copy of court order will do for name change it's likely you'll have to what amounts to suing the health department to change the certificate for gender (and a lawyer helps a lot there).

Good luck.