Sorry, I'm not a doctor, so I can't tell you if you should fly. I would recommend you ask your doctor. He might want you to have a treatment to take with you.
Several years ago, when I had retired, I had to fly on a long trip a few months after having had a heart attack. Toward the end of the flight I started feeling short of breath. I asked an attendant how high we were and it was 37000 feet. I know cabin pressure is supposed to be no higher than 10000 feet, but sometimes it's much higher than that. I didn't say anything because I was afraid I would be banned from flying. I was fine when we landed.
Airlines do have oxygen for emergencies.
I don't have COPD and am not on any treatment for breathing. My oxygen level is normally 100. I do take antibiotics when I get sinus infections though. They can get down in my lungs if not treated.
If I were in bad shape today I would not fly one of those long, high trips without something for emergencies. Sinus infections, if they're bacterial, for the most part clear up for me in a couple of days, when I'm on antibiotics. I usually have to take a sulfa drug. But ask your doctor!