In Texas, underage marriage is governed by Section 2.103 of the Texas Family Code. It is NOT a simple procedure. It requires filing a lawsuit, having the parents served. and the appointment of an attorney to represent you. You will have to convince the judge that it is in your best interest to get married.
I have put a link below to the Family Code. Scroll down to the Section I mentioned.
Lawyers charge clients based on the amount of time it will take them to do what you want. I have never been asked to file a petition like this. (I would probably decline to do so anyway), but based solely on how much time it would take, I would probably ask you for at least $1,250, plus court costs. Who knows, you may be able to find a lawyer to do it for a lot less.
An attorney will charge a client differing amounts to file suit depending upon the fee arrangement with each particular client. These arrangements are typically a contingent fee agreement or an hourly agreement. A contingent fee agreement is generally an agreement whereby the attorney represents the client in exchange for a percentage of any sum recovered by the client. In the hourly rate context, an attorney charges the client an agreed upon hourly rate for the work completed based upon the amount of time required to complete a particular task.