Susie, you do have your work cut out for you, but Chris has put you on the right track. The Orig. TX Land Survey (OTLS) polygon layer will give you the section, block, and survey info you will need to either visit the Harrison Co courthouse, or the county appraisal district online, from where you can do individual property searches. TNRIS is your one-stop shopping place for base map data for anywhere in TX, but assembling the ownership data will not be easy!
The Tx RRC will also let you search online for wells by section and block, so that will help you track down and start to assemble data. If your Uncle has some money to spend, you might try contacting P2 Energy Solutions, San Antonio (formerly Tobin). They sell well and ownership data, but they aren't cheap.
Midland Maps, Midland, TX, has a number of ownership maps in paper form for many TX counties, but I am not sure if Harrison is one of them.
GIS Division Mgr
City of Midland, TX