Do you have any pain from your mouth in the morning? Do you have a stuffy nose? Are your gums red or swollen? Do your gums bleed when you brush your teeth?
From what you describe it sounds like what my daughter goes through. She gets a minor bloody nose sometimes which drains down the back of her throat and can leave blood that is not swallowed in her mouth. She wakes with a stuffy nose and bad breath.
If your gums are red, swollen or bleed when you brush. Flossing and salt water rinses can help those heal up. If you grind your teeth at night and you have a loose tooth, that can irritate the gums and cause a small amount of bleeding.
My suggestion is to floss daily along with brushing twice a day. Use a salt water rinse as needed. Use just enough salt to taste it in a cup of water. Swish and spit a few times a day. And if you see no relief after a week or so, see your dentist to evaluate the situation.