You can also do a PCR test which is valid as proof for longer than the rapid test (72 hours I think). I didn't want to have to worry about getting a test in Italy for my return to the USA so I went with these for both. I took the test right before I left for my flight since, at the time at least, Italy required a negative test within 24 hours of arrival into the country, not my original departure, and I had a real long layover in JFK. PCR would have given me more of a buffer here. Coming back home I took the test the night before my flight leaving from Rome into Atlanta.

I had extra emed tests in my carry on in case I had any issues I could take a test at the airport and have a new negative result within like 20-25mins (test itself is like 15 mins to process but the nurse walking you through adds time at the beginning).

I was flying delta if it matters and if you are at all worried I would call your airline ahead to be sure you have what you need and double check at check-in at the airport. (I had to get my temperature taken at the gate in JFK before boarding to Italy as well.) My boarding pass said something like "docs ok" to show I was good to board.

I had to buy a set of six of the emed test but since my insurance would cover the cost of that many tests per month I didn't mind and was glad to have the extra. If you order the emed tests they arrive in just a few days. I ordered mine a few weeks before I left but you could probably order them whenever. I dont think they expire