Hi.. Welcome to HEALTHCARE MAGIC... I have gone through your query and can understand your concerns... As per your explanation it seems that you have infection and inflammation in gums which can be either concided to the marginal gingiva(gums) known as GINGIVITIS or have been progressed to the attached portion of gums to the underlying bone leading to damage to the bone also and the condition is known as PERIODONTITIS and both can lead to bleeding especially when there is some stimulants like brushing.. The dryness and blocked feeling in nose can be due to some infection or inflammation in the nasal lining and it is not related to bleeding while brushing.. You should consult a dentist and get evaluated and in case of gum infection Scaling of teeth and under the gums will be done by the dentist followed by Medication like Amoxicillin and Metrogyl and gum paint to apply over the gums.. Massage with Chlorhexidine containing gel like Hexigel helps.. Warm saline gargles should be done.. Maintain a good Oral hygiene and use an ultra soft toothbrush for brushing... Hope this information helps.. Thanks and regards.. Dr.Honey Nandwani Arora..