I don't know the rules in Texas for birth certificate changes, or in Wyoming for marriage. There are three sets of laws that are relevant for marriage where one person is trans: the law where you married, the law where you are (where you live, but also where you vacation/travel to, etc), POSSIBLY the law where you both were born (depending on the laws in the other two places). It can be extremely complex and, sadly, in most places it is somewhat unsettled law.
Depending on the jurisdiction, a person's sex is either what is on their legal documents, their chromosomes, their sex organs, what their parents assumed their sex was at birth, or a combination of these things. If the marriage is not a valid marriage (both people meet the state's definition of opposite sex) in *BOTH* the place you married *AND* the place you are when exercising rights of marriage, in the US, the marriage may be considered to not exist, legally. So the definition of sex where you are is important. Unfortunately the definition of sex isn't written in statute (there are administrative regulations for changing documents, but that doesn't impact anything other than those documents - states are not compelled to recognize a sex change for all purposes - they can recognize it on a driver's license and birth certificate but NOT recognize it for marriage, for instance)
I'm not a lawyer, but I strongly encourage you to NOT get married in a state that doesn't respect same-sex marriage unless you are both opposite sex, so I'd recommend waiting until surgery happens for that. Alternatively, divorcing and remarrying after surgery may be an option depending on laws. The reason for that is that a birth certificate doesn't legally make anyone male. A birth certificate is legal evidence that the person is male, but it's not as strong of evidence as the reality of the person's sex. For instance, if a non-trans person's birth certificate indicated that I was female (I'm a non-trans male), that wouldn't actually make me female legally. It would make things difficult for me, but it doesn't change my actual sex.
Also, in many places you can show documentation and get a license to marry based on that. But if the information isn't considered true legally in that jurisdiction, the marriage is void, even though a license is issued. There is a lot of consequences if that happens.
Take care to protect your soon-to-be marriage legally. Make sure you do your research and know the risks. I married my opposite-sex spouse without any concerns or regrets - but I do know what the risks are and that these risks and also that certain parts of the country would not recognize our marriage. I also know that, in much of the country, nobody knows if my marriage would be recognized. But I believe it would be recognized where we married and where we currently live, if it were ever challenged.
It's for these reasons that I am looking forward to the Supreme Court finally deciding that sex/gender is irrelevant when it comes to the definition of marriage.
