Jack2007,
I looked up the flight crew of your flight on 4/12. I don't know them, but I'm sure they're very safe and knowledgeable; I haven't met a captain at Allegiant yet who wasn't. I am based in Las Vegas, so I don't get to fly with the FLL crews.
Our flying is very relaxed, we go out and back to the same airports all the time, so we are highly familiar with the routes, ATC, and the airports. Most captains even know the frequencies by heart before ATC assigns them to us. There are rarely any surprises.
I have personally had my mother, best friend, aunts, uncles, cousins, and other friends fly on Allegiant and I have never thought twice about it.
I suggest you let the flight attendants know about your fear of flying when you board. They are very understanding and helpful and will do anything they can to alleviate your concerns.
Please remember that only you can decide if you are okay to fly. If you start to feel ill, nauseous, faint or just aren't feeling good, please consider postponing your flight until you are ready. We want to ensure that you have a safe and enjoyable experience.