You dont need to be a natural-born athlete to ride 2x11 miles. It is a quite reasonable distance to ride. I used to ride 2x12 miles in London, do a full days work in a busy shop, do a martial arts class and ride home. Ive never seen myself as an athlete.

You need to learn how to ride like a vehicle. The single most important thing you can do to make cycling safer is to learn and practice safe cycling techniques. You have already tried stupid cycling and understand the pitfalls of this method of riding.
You dont need to spend huge amounts on fancy bikes. You should be able to pick up a decent used bike for less than $200. You need to buy a suitable style and size and something that is not worn out. The Sirrus is a good style of bike but you can get similar bikes from other brands.
You have to kit the bike for all-weather utility riding, with luggage rack, fender, decent lights and tough, puncture-resistant tyres.
To protect yourself you need high visibility top, helmet, mitts/gloves (to protect your hands from crash damage). You also need some 3rd party liability insurance which may come with your parents house insurance or with membership of a cycling organisation.
Apart from the odd hurricane, its hard to see how Florida weather would preclude you from riding. You can buy clothing appropriate to the conditions.
Cycling is just a good way of getting around but it is addictive so dont let it distract you from your studies. Einstein used to do a lot of thinking on his bicycle.