Bloody nasal discharge can be caused by allergies, sinusitis, infection or blunt force trauma. In common cold, the mucus membranes make excessive mucus that may have spots of blood. Constant nose blowing and irritated nasal passages can also lead to bloody mucus discharge. There’s no cause for alarm as it will disappear with the cold.
I do have sinusitis that's why I hate getting a cold. Wish I knew some ways to prevent it from occurring though. I take vitamin C and get enough sleep but there are nights that I cannot sleep as much as I want to.