Are you coughing a lot?
It depends on what it looked like on how serious it is.
If it was bright red, or frothy and blood streaked, that's probably from a chest infection, and not that alarming, though you should see your doctor.
If it's dark red, or looks like coffee grounds, that's from the digestive tract, and could be very serious, and needs to be checked out right away - that warrants a trip to the hospital/emergency dept if it happens again, or at least an emergency call to your doctor.
It isn't from swallowing post-nasal drip, though.
Since your nose was bleeding, and you are coughing up stuff, I'd wonder if you have a sinus infection, or perhaps bronchitis. Of course, it's important to rule out COVID19. Give your doctor a call. Any time you cough up blood, it's worth at least a call to your doctor.
Let us know what happens, and feel better soon!