It is possible that the source of the blood is a
noseNose fracture bleed, with blood moving in both directions; forward and out the
nostrilNostril nasal decongestant and backward into your
throatCancer - throat or larynx
Throat swab culture. The answer to your question depends on your age, general health,
smokingQuitting smoking
Smoking - tips on how to quit
Smoking and copd (chronic obstructive pulmonary disorder)
Smoking and smokeless tobacco
Smoking hazards history, the presence or absence of fever or chills, etc. If you are age 30 or less and especially if you are a non-smoker, you can safely afford to wait a couple days for spontaneous resolution of the bleeding. On the other hand, if you are an older individual and/or a cigarette smoker you should see a doctor now; one who can and will examine your nose and throat with an instrument called a fiberoptic laryngoscope. The same exam should be conducted if there is no abatement of the bleeding over the next couple days and immediately should the bleeding worsen.
Another, common cause of the bleeding you have experienced is the use of nasally inhaled illicit drugs, most notably cocaine.
Once again, if the bleeding does not cease spontaneously in a couple more days or if it worsens, you should see a doctor for evaluation of both nose and throat, and your lungs by examination and a chest x-ray.
Good luck.