dude I feel your pain! I was born in Texas too... haven't lived there in 18 years and they still make my life a living hell when it comes to trans laws.
Anyway... The only way to find out if you need your birth certificate to get a marriage license in your state is to call your local city clerks office to find out what your states individual law is... everywhere is different.
When it comes to changing your birth certificate... Texas will only give you a REVISED version of your birth certificate for you which just gives you an additional paper that says you are male now but you were once a female.
Because of this some states WILL NOT grant you a marriage certificate. They will see that you are trans and have changed your gender and deny it. Seriously messed up I know but it's happened (I'm in the wedding industry so I've witnessed these stories first hand). I would ask the clerks office about this when you call to see were they stand on this issue...
Anyway, you don't always need surgery to get your BC changed. Some endocrinologist's will write THE LETTER for you instead. Anyone I know who has changed their gender marker has done it this way and they've never had a problem with it... so talk to your doctor about that option and if they would be willing to do that.
If all else fails there is always domestic partnership/civil unions... I know its not as awesome as actually marriage, but if your state allows it, than its the next best thing.
hope this info helps, congrats on the wedding bro!