Take melatonin with you so you can take it around 8 pm the day you arrive and get a good night’s sleep. Have vitamins with you as well. Try to have a balanced meal before you leave and when you arrive. Be super hydrated the entire trip, it will lesson how shitty you feel. Move around during the flight so your circulation isn’t suffering. There’s really not much other advice I can give you for the flight, except to do your best to pack light so you aren’t extra stressed with several pieces of heavy luggage, which does make a difference. And the morning of your work, get a full meal, a nice coffee, and go home and rest immediately after your finish. You got this.
I don't think Melatonin is going to do anything for someone in a single one-off scenario. A very large percentage of people get virtually no benefit from a single one-time use of Melatonin. Melatonin is not a sedative, it's a hormone that helps adjust the circadian rhythm, so it helps with timing your sleeping cycle. It absolutely will not help someone sleep in a high-anxiety scenario. OP needs an anti-anxiety pill of some kind. Something that will sedate them for the flight.