Hi Maria and greetings from a relative newbie,I can only tell you what I have learnt here also,apologies if you already know any of this but I might as well explain the whole thing.
Most figs exchanged here are 'self fertile' (Parthenocarpic) known as Common type figs,they will produce figs without pollination by the fig wasp,they will make either 1 crop(these are called called Unifera varieties) or 2 crops (bifera varieties).If these are pollinated generally it results in changes in size,colour and flavour compared to what you may get if they aren't pollinated,but the main thing is either way in your area with these varieties and no wasp you should get either 1 or more likely 2 crops of figs to ripen.
There are many fig varieties that need the fig wasp to produce any figs at all,those are referred to as Smyrna type figs and generally when giving details about a fig here if the variety needs pollination people will say "this one needs the wasp" or "it's a Smyrna".I think in the USA only California has the fig wasp,it was introduced there to help create a fig growing industry.
There are also intermediate types called San Pedro figs,those will ripen a Breba(early/first) crop without the wasp but without pollination the main crop won't ripen and will drop off(which is OK if the Brebas are good enough).
To top this biological confusion off,there are also 2 different fig 'genders'.All of the above are regarded as functionally female(receptive to pollination).There are also figs which are functionally male (which produce the pollen for thof fig wasp to deliver to the 'female' trees),those are called Caprifigs,they are only really useful for folks who have the wasp in their area as they provide a home for the fig wasp and pollen for pollinating.
So in Texas what you really want are 'common' figs as you don't get the wasp.Are there particular varieties you are concerned may need pollination by the wasp?.If you post here I'm sure someone will know straight away if it needs the wasp or not