There aren't any cave dives near Mobile. The closest would be in Florida. While there are some small ones near Defuniak Springs, FL, the closest good ones are near Marianna, FL..
If you are still interested, take an Open Water SCUBA class, There should be dive shops all along the coast. Once you get comfortable in the water, go to
http://www.nsscds.org, and find the instructor list under Training. There are 4 levels of training. Cavern in the first level, and you learn to safely go in a cave, but remain in sight of the entrance. If that doesn't scare you off, then you can take the next three levels, and get progressively farther at each level. FWIW, there are a lot of unexplored cave diving sites in N Alabama. I personally have 50 unchecked leads.
The cavediving forum here isn't used much. If you want to try a more active cavediving forum, try
http://www.cavediver.net You should be able to get some good advice oh how to pick an instructor. I will tell you now that if cavediving is what you plan to do, just rent gear for your Open Water class. Almost none of the gear you use there will be useful for cavediving. If I were just starting out, I would try to find an instructor that teaches Open Water sidemount, That course is taught using cavediving gear. Feel free to PM me for advice.
Any opinions are personal.