Use this website to determine what visas etc may be necessary for your particular case, taking care to enter your travel such that each country you pass through is input.

https://skyteam.traveldoc.aero/

Note that if you are travelling on separate tickets [if you booked your Italy to USA and Egypt to Italy tickets separately], you will be considered not as a transit passenger and would then also have to meet all the requirements for entry into Italy/Schengen.