Learning about the snakes in Texas could reduce your anxiety. Venomous snake bites are extremely rare and half of the bites are dry bites, indicating that there was no venom injected. The main aquatic species of concern is the western cottonmouth (Agkistrodon piscivorus) commonly called the water moccasin. They can be very aggressive and are my least favorite snake. I have had them try and eat fish off of my stringer. Besides the cottonmouth, other venomous snakes, like copperheads, rattlesnakes, and coral snakes, could be encountered around aquatic resources. You should learn how to identify those snakes.
Most of the snakes you encounter will be non-venomous. There are several very common aquatic non-venomous snakes in Texas. They will all bite, usually smell bad, and are aggressive. Thrashing a rod tip in the water will often attract them. They are usually just looking for a dying fish.
Stay aware of your surroundings while fishing. There are horror stories out there, and I have my own, but if you are afraid of all the things that can happen, you would never go fishing or even leave the house.
https://www.dshs.texas.gov/idcu/health/zoonosis/Animal/Bites/Information/venom/snake/