Take it from a fellow Texan--I am just outside of Austin....you have a mesquite thorn in the tire. My tractor collects them. Most of the time you end up with a slow leak and then a flat.
Since your tires are not filled, I do recommend the green (or some is red) slime. You will need to get several of the big gallon sized.
Also, I would also highly recommend you get yourself something like this:
Amazon.com: ORCISH 7Pcs Tire Repair Kit, Heavy Duty Tire Plug Kit for Car, Truck, RV, Jeep, ATV, Tractor, Trailer, Motorcycle - Universal Tire Repair Tools to Fix Punctures and Plug Flats: Automotive
SInce it is not a high speed tire, you can do a plug without taking the tire off. It is not as good, but it works for most tractor use.