Food allergies often worsen with repeated uncontrolled exposure, so it can become very dangerous very fast for you to be exposed to seafood. Obviously you need to tell your family because you need their support in preventing exposure for you. Since you already have had multiple exposures eating chicken at a seafood place, if you willingly accompany your family to one, most likely you will simply have another episode. It is important not to go in to such an environment.
Luckily, there are many good places to get food in Florida. If you do some research ahead of time, perhaps you can find a restaurant that has outdoor seating; in Florida most days you would have good weather for it, and you can look at online menus ahead of time to be sure there is something you can eat too. I don't know if your level of sensitivity would allow even that much exposure, but perhaps it is worth a try. Outdoors there would be fresh air, and less likelihood of the strength of exposure you would get in a confined space.
You can also just plan to get food somewhere to eat in a park nearby where everyone else goes to eat seafood. If there is someone in the family who doesn't particularly care for seafood, maybe they would keep you company.
Realize that it is a whole lot easier for your family to accommodate your dietary needs than it is for their vacation outing to be broken up with having to call an ambulance and spending the afternoon in an emergency ward.
Describe your symptoms to your parents and tell them you need to avoid exposure to seafood. Find out what they have to say early on so there is time to plan for how to manage the situation.