In Texas they are simply called County Courts (technically Statutory County Courts) and they handle civil cases over $10,000 and up to $200,000.
To find yours, google (your county's name)County Court.
If you are willing to sue for only $10,000 and waive the rest you can use your local justice court (small claims). It's less formal and you won't necessarily need a lawyer.
Might be wise to go that route since you are unlikely to ever see a penny from this low life even if you win the lawsuit. At least you avoid paying thousands in attorney fees that you don't get back.