Cat nose bleed

I’m still new as a cat pet owner. My two cats we’re fine, eating, playing, doing cat things. After a few days one has started to sleep ALL day gets up and eats and then if he doesn’t go back to sleep he is constantly following me around having to touch me and meowing very loudly. He has watery eyes one day had discharge from eyes, sneezing, and has had two nose bleeds now. I was pretty alarmed with seeing the blood. He has a vet appointment coming up for his first shots and neutered but just wondering if anyone has dealt with anything similar and if it turned out to be okay.

Also will add they are two cats that roamed

Indoors and outdoors that were from a cat hoarder in the family.