It will do you no harm to take aspirin regularly. for just that length of time. The limit is 12 a day for the full strength tablets, which I seriously doubt you will reach. Aspirin thins your blood a bit, which would mean you will be less at risk for circulation problems brought by lengthy sitting on an air plane. It also means they ask you to stop taking it before operations and tooth extractions. I wouldn't worry!

The aspirin's anti inflammatory effect may be a curative one for your problems.