Hi welcome to Health care magic forum.
Thanks for choosing H.C.M.F.
As you describe your 19 year daughter had stomach pain, watery brown diarrhoea
, black purple vomit, When she blows tarry black on the tissue.
The description suggests that there is heavy infection in in the intestines, with probable blood oosing in intestines, it happens when there is much cramping or more infection. Nasal discharge dis colouration is secondary to the regurgitation of the black vomit.
If the infection is controlled effectively every thing will be cleared . So i advise you to consult a physician for diagnosis and treatment.
Wishing for a quick recovery.