That there is a tingling in my hands. Should I try one of those carpal tunnel wrist splints?

C ur MD first. See a doctor before self treating for a condition which could be indicative of a more serious underlying disorder.
Yes. That is a good place to start but if it persists then i would see you doctor for further treatment amd make sure it is not something else.
Yes. Carpal tunnel syndrome causes numbness and tingling in the thumb index middle and ring fingers. If these are the symptoms you are having you can try a wrist brace at night that help to take the pressure off the nerve. If the symptoms do not resolve within a few weeks to see a doctor for a full evaluation.