Are you doing short haul? I do 2-4 flights most weeks around UK/Europe, each flight being an hour or 90mins or so. There is lots of hanging about at airports/lounges, that doubles the travel time. As the only option is usually domestic economy seating and little if any time change much of the advice above may not apply.
I treat it as the bus to work as it is just public transport. Unfortunately I recognise your problem symptoms. It is worse when I have done more flights (weeks with 4-6 flights), I invariably feel ill then. I put it down to exposure to airborne bugs etc / close confinement with varied and constantly changing people. More flights rapidly increase your odds of contact with a bug.
I seldom drink alcohol as I usually pick up a hire car on landing, and am careful with public feeding areas. Regularly wash hands etc. I still get ill.
When I stay at home and seldom see or deal with other people I rarely get ill.
If you find a magic cure, do come back and let me know.