How To Cure Large Bug Bites From Bicep Into The Wrist?

I'm traveling from work and am in Ft. Lauderdale. Took a walk on the beach last night and hours later noticed several bug bites on me. I am very prone to bites even when no one gets bit. But these were large...bigger than a silver dollar.
The one on my right arm on the bicep itched all day but didn't think much of it. Then in the last hour my entire right arm became throbby and numb, all the way from the bicep into my wrist and hand. I don't want to over-react and rush to the hospital. But I also don't want to neglect anything that could be serious. Any thoughts?