Well, the nosebleed thing is probably due to the change in humidity as per the changing of the seasons. I encounter about a week-long period twice a year where I get 3-5 nosebleeds for no reason and they are always around February-March and October-November when the weather changes. The first time it happened I mentioned it to my doctor back in the States in passing and he brought up the probable cause of humidity change.
I, too, have been getting black shit in my nose when I blow it, but that’s too be expected in pollution-high areas. I don’t recommend exercising outside. My gym membership just ended and I didn’t renew it because I thought I might try just exercising in my house and running/jump roping outside. I ran about 3 miles two days ago and now am pretty sick for the first time all season. My immune system is pretty baller, so I’m blaming pollution for that one.