This question comes up here periodically, so if you use the search function at the top of your screen you can find some good tips from our previous discussions. But, generally, there's some basic things I do that might be helpful, although I'm guessing some of this may be repetitive to you...so here goes. Bring an Epipen and a back-up one so that if you end up using it you're not traipsing around looking for a replacement. Bring your own Benadryl - they do not sell this in Italy.
When I travel, I take a daily Zyrtec, as it provides a little wiggle room coverage, I think. This might be especially helpful for the peanut/almond/walnut allergy. If you run out of Zyrtec, you can buy it over there in a pharmacy.
I carry an allergy card that lists my allergy and specifically states that it's a life-threatening allergy. I really like to stress this because sometimes I worry that people just assume I'm "fussy" or that I have an intolerance to something.
I mostly find it stressful to try to describe my allergy in a restaurant setting in a foreign language so I usually rent an apartment so I can cook my own food. I read a lot of labels in the grocery store and can usually find my problem food.
I think all of those nuts will show up in your restaurant meals there....we're served walnuts in salads all the time, there's nuts in the pesto often. While my allergy is not to nut products, restaurants are just tough and require a lot of vigilance. I've had a lot of ordering failures....even after telling my waiter about my allergy this past April, he brought me a salad 5 minutes later with that very item in it!
I try to stick with basics in any eating situation. I eat like a 8-year-old when I travel. Pizza. Pasta with pomodoro sauce. Gelato. More pizza. Macaroni and cheese.
It all works out but it's always a relief to get back to my hometown restaurants, where I know what dishes I can eat.