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Yes, you should be concerned. Nose bleeds too should be investigated. Once there is bleeding from nose, it is natural to swallow some blood, which a person can vomit. Bleeding from nose can be due to foreign body in the nose, nasal polyps, allergic rhinitis, high blood pressure, sinusitis and dry nose.
Smoking, alcohol use, gastritis, acidity, tumors of stomach and food pipe, bleeding gastric ulcer, cancer of stomach, erosion of lining of food pipe, bleeding veins at esophageal (food pipe) sphincters etc all cause vomiting of blood. The presence of these conditions can aggravate the vomiting of blood after a nose bleed. This can be fresh red if coming from a place above the stomach. It can be brown or coffee colored if coming from the stomach.
The other possibility is that you are coughing up blood. This can be due to bronchitis or pneumonia, lung cancers (especially in smokers), tuberculosis, bronchiectasis, pulmonary embolism, or fungal and other infections. Since you have phlegm, lung conditions including asthma should be investigated.
Discuss these possibilities with your doctor. It is difficult to comment beyond this without examining. A comprehensive investigation is required keeping all the points in mind. Please let me know if there is any thing else and do keep me posted. Take care!
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