Even though you were breaking the law by driving without insurance if the other driver was at fault you normally will not be liable for the other party's damages. The at-fault party though will likely have to pay for your damages; this means you generally should be able to make a claim through their insurance policy for your vehicle's damages.
You will be in trouble if cited for not having insurance. In Florida if you do not have proper insurance you can lose your driver's license and license plates as well as have to pay large fees to get them back.
Do not drive on the roads again before being insured. Get a cheap car insurance quote for FL through us.