Real Estate Law
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There is a process for appealing your property taxes. Section 41.44 – Notice of Protest http://www.statutes.legis.state.tx.us/Docs/TX/htm/TX.41.htm
Can you tell me if you used a loan/mortgage to purchase the home and if so did your lender perform an appraisal of your home? The appraiser should have the best information on the square footage so I am suspect of them telling you that they "attempted to get measurements from the previous owners" as they should have had measurements when the home was built and permits where applied for.
You would start by filing a protest. Have you filed anything yet?
Do you have any additional questions or information for me. It would bet pleasure to continue to assist you.