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!
What to do depends on how often, and how severe the bleeding is. The cause is likely to be dry air. Which can result in more frequent bloody noses in heating season, and the latter part of the air conditioning season... The dryness inside the nasal passages can be irritated and promote cracking and bleeding. Nasel gel such as NeilMed (TM) can be a great help! If you still get frequent nose bleeds, See an ENT specialist. In my case the doctor did an electrocauterization (office procedure) to treat it. The first time he did it the treatment lasted 17 years for me. (The doctor joked "60,000 miles"). When I had four bloody nose events in one week, I called and had the 2nd treatment done this spring. Well worth it if you need it!