There are some companies that were at the soapmaker seminar I went to in Georgetown, TX the summer before the pandemic. I will try and find some links. There was a candle & soap supplies company in Tyler, TX (my niece used to live there), but I think they moved to Missouri. Muddy Soap Company in Houston had a fire last week and lost all their inventory, as well as extensive damage to their warehouse, and don't have an estimate of when they will be open for business again. (They were one of the vendors at the seminar I mentioned.)
Lonestar Candle in Keller, TX only sells MP base, and no oils other than waxes. If you wanted to try
GW415 soy wax in your soap, which several of us do, you could purchase from them. Also beeswax. But that's about it, other than some silicone molds for individual soaps.
AAACandles in Dallas, also sells
GW415 soy wax, but not much else as far as soaping oils.
Southwest Candle - Soap & Candle Supply in Mesquite, TX has oils at least, see this search result for the list of carrier oils:
Carrier oils.
World of Aromas in Carrollton, carries butters & some oils, as well as fragrances. I can't vouch for the fragrances, but I'd use the oils without worry.
Texas Natural Supply in Austin carries a variety of oils, butters, and various other supplies. Oops, others already listed them.
One other source for information about suppliers in Texas might be the Lonestar Soapers group, but I don't know if you'd find out any more there than you will here.
If you can't get the basic oils you want at local grocery stores, you can also look for restaurant supply stores. Some of them have what they call 'Cash & Carry' stores where the public can also walk in and purchase foods they sell to restaurants. The cost to the public is usually slightly higher, but still less than the cost at most Big Box stores. I have purchased oils at the one we used to use for restaurant supply. The oil choices are usually pretty limited, but it is another source.
I think that's all I can recall from my limited experience with suppliers in or around your part of Texas.