Generally, no. A release agreement basically states that the case is over, and you cannot sue the person released in the agreement. It is important to understand that when you resolve a case by accepting money from the insurance company for your injuries and by signing a release that you are completely resolving the case. Thus, generally, you cannot sue the insured person who you released.
There are a few insurance companies in Florida which make you an offer within days of the accident. I generally do not recommend accepting these offers as you do not know about the impact of the accident so shortly after the accident. If you truly have no pain and ultimately have no pain and no injury, then it may be a good deal but how can you know that 48 hours after the accident. These offers are almost always great deals for the insurance companies that make the offers in my experiences. I have seen cases where the client settles their case for $1,200 and in fact after their car insurance pays the hospital bill (and given the client had a $1,000 PIP deductible), the client owed more than $2,000 to the hospital – NOT A GOOD DEAL! You should consult with an attorney BEFORE YOU SIGN AND SETTLE YOUR CASE!