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The inside of the nose is lined with tiny little blood vessels. When a person has a cold or allergies causing a runny nose the inside of the nose gets red and irritated (inflamed). This swelling inside the nose and irritation causes the thin lining of the nose that covers these tiny blood vessels to thin even more making the tiny blood vessels closer to the surface. Blowing the nose very hard can cause further irritation inside the nose by dislodging mucus and possibly exposing these tiny vessels resulting in bleeding. If a person is getting frequent nosebleeds they may have tiny little clots that have formed that have stopped the bleeding previously. If they then blow their nose very hard they could dislodge one of these tiny clots and the nose will start to bleed again.