I noticed that when I had a cold during high school. Weight training class would clear my breathing for a little while. Then I think by next period, I felt crappy again.
That is because during exercise the body produces adrenaline, which happens to be a natural decongestant.
Sauna or steam, maybe a massage, soak in the jacuzzi chased by some bourbon, honey and lemon and lots of sleep is best cure in my old age now. PT & six mile shuffle did work as well when active duty. Yet that was not as much a choice for me as it was my NCO’s. But the exercise did work the illness out faster for me. Even the flu was afraid of my NCO’s !