Nobody ever wants to get sick, and for sure not on vacation. But if you are in trouble, you will want to have read what to expect in advance.
Western Europe, to which Italy belongs, is highly civilized. This means the medical system is very well established, with the usual structure of first aid services, local hospitals and major health centers that we know from the States.
Treatment is usually quite good, although nurses are severely underpaid and traditionally rely on the families of patients to pitch in with the assistance. Rarely will you find anything that doesn't look right or feel right. And if you do, try to get out of the place and get into the next one.
The list of medicines you can get over the counter is much shorter in Europe that in the States. To you this means you should try to get all generics you will need, and try to get prescription for OTCs you typically use.
Food is as safe as at home (even when it looks funny). Don't eat raw meats or fish, as Italians wouldn't (the thought of sushi is a bit icky to most Italians, say). Anything else is free for the biting.
All in all, don't forget: even if people talk funny and act funny and drive like madmen - it is one of the cradles of civilization, still one of the most civilized and proud nations on this planet. And you can feel just as safe as you would at home - save pickpockets, of course!