The quantity of the blood spitted might have been useful. The frequency of the vomiting and the containment of the vomited fluid (food, bile, blood) are also important. Without this additional information it is hard to give a definitive diagnosis.
The blood when clearing the throat might be caused by inflammation of the throat tissue. When you clear the throat, you might be mechanically damaging the mucosa which is manifested with spitting blood.
You might want to visit an Ear, Nose and Throat specialist to check for the throat and nasal condition. If the vomiting is too frequent and contains blood, then you might be experiencing chronic gastritis (chronic inflammation of the stomach) or ulcers. For this condition a specialist for the upper gastrointestinal tract might be helpful. If the vomiting is accompanied with nausea that does not stop after the vomiting, then the whole situation (including the headaches) might be related to neurological issues, for which a visit to a neurologist is recommended.
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