Hello,
Thanks for using HCM.

It is difficult to know the site of bleeding without proper examination of oral cavity.

In many of the patients with bleeding problem there is deficiency of vitamin C that leads to fragile blood vessels and bleeding.

For examination of oral cavity see a dentist in person. He will examine oral cavity and do some coagulation tests to determine the coagulation profile which includes bleeding time, clotting time and INR.

Before you can get an appointment with dentist kindly use vitamin C capsule or increase the citrus fruits in your diet.

Thanks for your query, I have gone through your query.
The bleeding in the oral cavity while brushing or at rest could be because of the gum infection, or any cuts in the oral cavity or pulp polyp or any bleeding disorders like idiopathic thrombocytopenic purpura. Consult a oral physician and get these things ruled out. Get a complete blood investigation along with INR to rule out the bleeding disorders.
If any gum infection then get your teeth cleaned and use topical gum astringents like stolin gum paint.
if pulp polyp is there then get it root canal treated.
If bleeding disorder is there then consult a general physician.
I hope my answer will help you, take care.