At least you are headed in the right direction! South!! To the sunshine. Safe travels...

Usually, you can tell by the tag they attach to your bag. If it says both destinations, they usually it goes all the way through, if it just says one then you may have to pick it up and re-check it. This what was happened when I flew to London via Germany once. We changed plane then too.

Alice -- you are basing your info on a transfer through European airports, which has nothing at all to do with this question. When Arriving the the US from overseas (Ireland is an exception), one has to collect their bags and then drop them off again.

If it says both destinations, they usually it goes all the way through,

Nope. That statement is not true for entering the US from Mexico on a US passport - the case of this question. When you go thru Customs you have claimed, gone thru the checkpoint, then rechecked the bag, even when if/when it tagged for the final destination (in this case in Houston but tagged for Boston).

Happy trails!