Turtles can drown! I know, freaked me out too. Not all turtles are great swimmers, Mud turtles are one of those turtles.
I HIGHLY recommend finding a local vet that takes reptiles AND an emergency vet service that does reptiles. That peace of mind was priceless.
We had an adventure with Superworms. She is not large enough for superworms. I thought she was going to choke and die, and I was frantically googling how to do Turtle CPR. Here is what I found:
1) Immediately remove the turtle from the water. Gently grasp the back of the turtle’s head and extend the neck.
2) Tilt the turtle so the head is facing down towards the ground. Open the mouth if you are able. If the turtle has drowned, water will probably begin to drip out of the mouth/nose. Continue to hold the turtle in this position until water stops coming out.
3) Place the turtle belly-down on a flat surface with the head facing you (the neck should still be extended). Pull the front legs straight towards you.
4) Without letting the legs bend at the elbows slowly pump them in and out of the turtles body. This will push the internal leg muscles into the lungs and force out any remaining water. Continue pumping the legs until water stops coming out.