Sore throat, runny nose, coughing, sneezing, constant vomiting i can't keep any food down, what could this be?

Viral infection.: You do need to be seen with the constant vomiting as you are at real risk of severe dehydration and electrolyte abnormalities.

Viral infection: Sounds like you have a cold, maybe a little more severe than average given the nausea and vomiting. Drink fluids, take aspirin or acetaminophen. See a doctor if the vomiting continues more than a day or two and you can't keep anything down, or if you get dizzy or lightheaded, or if you develop high fever (over 101F/38.5C). Without those problems, this doesn't sound serious.