Yes - if you are seeking contempt, it is two years after the child hits 18 or the support terminates. Contempt is jail time. If you are simply seeking the money, you get 10 years from the child's 18th birthday or the date the support ceases in the order.
You might as well move on it... you are going to have to serve the obligor and figure out how he is going to pay it... there are few people that can pay that kind of money all at once, but some sort of payment plan could be arraigned, and if you get it in judgment form, there are ways to collect under TX law. Feel free to ask questions.
Disclaimer: This answer is intended for educational or informational purposes only and should not be considered legal advice nor forming the attorney client relationship. This lawyer is licensed in TX and you should consult an attorney in your state before moving forward.
Yes there is a deadline. Mr. Harding is correct.
I also think you shouldn't wait to seek the back child support. Also, many times in a situation like this, the law will allow you to recover the cost of your attorney's fees from the other parent.
I think it's time you hire a family lawyer and take the other parent to court.