Photos, get estimates on the home and any improvements made, the assessor has the neighbor's home; see if she'll print out their assessments for you. Ads of local homes for sale.
Be sure, if qualified, you have Homestead Exemption.
In Texas most appraisals for property and other property information are on-line. Check to see if your county has a web page. It will tell you how to access the tax office. Select properties similar to yours, then go online and check out their apraisals for comparison.