Check out this link http://www.co.galveston.tx.us/jp1/documents/eviction/Eviction%20Information%20in%20English.pdf
It provides the details of appealing an eviction starting on page 4. I suggest hiring an attorney.
-Michael R. Juarez Law Office of Juarez and Schaeffer PO Box 16216 San Diego, CA 92105 (619) 804-4327 www.jslaw.org Mike@jslaw.org This posting is provided for “information purposes” only and should not be relied upon as "legal advice." Nothing transmitted from this posting constitutes the establishment of an attorney-client relationship. Applicability of the legal principles discussed here may differ substantially in individual situations or in different jurisdictions.
To start, you'll need to file a notice of appeal, and post a bond. Talk to the JP court clerk.
If you think you have a good case, I strongly suggest you hire an attorney, otherwise all you're going to do is delay the inevitable.