Legal Question in Family Law in Texas

While I do not know the details of how this came to be and where the dad is, generally speaking in Texas you will have a chance to request custody very soon.

Under the Texas Family Code, a non-parent party may file for conservatorship of a child if the child has been voluntarily relinquished into their care by the child's parent for a period of one year or more. At this point, since the child has been with you for 10 months, it would appear you only have a couple of month to go before you qualify to petition the court to appoint you as a sole or joint managing conservator of the child, with appropriate possession periods laid out as between you and mom and even an order of child support.

Hope that helps.