What you're describing doesn't sound like a bug bite, but I see no pic to get an idea what it looks like. I don't really think a bug bite wold have him scared enough to not want to go outside - however an animal bite certainly would. I would get him to the vet and find a way to make payments if you don't have the money up front. I don't mean to be an alarmist, but it could be serious, and I wouldn't take the chance that it isn't. Good luck, and keep us posted please.