Can I still sue for injuries suffered in an auto accident AFTER I've signed a release, and sent a check by the insurance co.?

The short answer is almost certainly not as to the at-fault driver's insurance company. Assuming no coercion or fraud, you had now entered into a contract with the insurance company in which you received money in exchange for a release. If you do have ongoing injuries, you may make a claim under your own uninsured/underinsured motorist (UM/UIM) coverage if you have purchased it from your insurance company. Unfortunately, this coverage is not required under Florida law and many Floridians go without this most valuable coverage. If you are injured by a driver with no bodily injury insurance or not enough, your UM/UIM insurance carrier stands "in the shoes" of the at-fault driver and you may make a claim. But, there are also notice requirements in any UM/UIM contract, so you would want a qualified plaintiff's attorney to review before proceeding down that route. If you don't have UM/UIM coverage, purchase it for the future. You would be very surprised how inexpensive this critically important insurance coverage is.

It is very UNlikely that you would be able to sue for additional money after you have signed a release. Always higher a lawyer before signing a contract, especially a release. The release releases the insurance company and its client from any and all further obligations regarding this auto accident.