If you are in a traffic accident, it won't be long before you'll be talking to insurance adjusters on the phone. Sometimes, the adjuster calls before you even get home from the hospital.
What should you say to them? It depends. There are good adjusters and bad adjusters.
You should definitely talk to your own insurance company's adjusters. In fact, if they don't call you, you should call them right away to report the crash. Even if you were partly (or wholly) at fault, it is important that you put the insurance company on notice of the crash. That way, they can do what they are paid to do, which is to protect your interests.
In Florida, as in other "no-fault" states, your insurance company will assign you a "claim number," which will allow you to get medical care on your insurance. Remember, your auto insurance is "primary coverage," so you have to exhaust your no fault insurance ($10,000) before you can start charging medical treatment to your healthcare coverage.
So in short, talk to the adjuster from your own insurance company. If you don't they can deny coverage. And besides, they are looking out for you.
On the other hand, the adjuster from the other guy's insurance company is out to get you. His only aim is to undermine any claim that you might make. Do not talk to him. If you receive a call from the other person's insurance company, merely saying an obligatory "I'm fine" after the customary "How are you today?" can be used against you later.
The best thing you can do if you are called by an adjuster for the other side is to tell them that you are in the process of getting a lawyer. That will do two things: It will encourage the adjuster to get off the phone with you right away, so as not to be accused of tampering, AND it will encourage the adjuster to take your case more seriously, since you have decided to bring in a lawyer to represent you.