I agree with the sentiments of others. Italy isn't exactly a 3rd world country, they will have care available, but I guess it may be more costly as you'd be paying twice.
I see you're in the USA, shame! If you were in the UK a cheap flight back would only be about £50, you could come for a week, have a checkup, and go back!
I guess it's just bad timing. Whatever you decide, only you know best, so good luck

I'm sure if you did leave them on, you could get treatment if you needed it, but I would talk about it with your dentist, find out what the risks each way are, and then make a decision.