As you read this response, please bear in mind that this is a public forum on a website, and that this answer does not create an attorney-client relationship, nor is anything said on this site confidential or covered by privilege. As with anything in the law, there are exceptions to every rule, and you need to consult an attorney in your area for the best answer. Also, because of regional differences in practice, even within a state, what works in one area may not work in another.
Under the Texas Code of Criminal Procedure, the Harris County Sheriff or his representative has ten (10) days to come to Brazoria County to get your son and take him before a Harris County judge. If he has not done so by the eleventh (11th) day after the arrest, Brazoria County must release your son without bond.
Once he was arrested, he was supposed to have been taken before a Brazoria County judge, and the judge is then supposed to notify Harris County that he has custody of your son. Whether or not that happens, though, Brazoria county has to release him if he has not been moved to Harris County and taken before a judge there by the end of the tenth day.