How do I get joint custody/child support in Texas?

If you have not established paternity of this child you will need to do so as well as seek visitation. Child support will be established. File a petition in suit to affect parent-child relationship in the state and county where mom and child live. Go through proper procedure to serve her with the petition and notice of a hearing set in the court. Then travel to court and appear at the hearing with proof of proper legal service, asking for the court to name you as the child's father and to establish visitation. A lawyer in the state can make this easier than doing it yourself.

Two ways. You can hire an attorney in Texas and have a temporary orders hearing and a visitation order within a couple weeks. You could apply for child support services with the Texas Attorney General. They are free, but can take a year to get to your case (assuming your case doesn't fall through the cracks). The problem is the AG's only interest is getting child support started. They will include a standard possession order if the other party doesn't object--if they do object, you are back to hiring your own attorney.

You would file a parent-child relationship in Dallas County. You should try to retain family law counsel in that area.