Abdominal pain and throwing up

All the symptoms you have experienced are characteristic for gastroenteritis or stomach flu.
It is of acute onset, and usually lasting from 1-6 days, but, with symptoms being more prominent for the first 3 days.
The redness of your eyes is due to broken blood vessels.
Conjunctiva (the thin, moist, transparent membrane that covers the white part of the eye) contains many small, fragile blood vessels that can be easily ruptured or broken.
Strenuous and repeated vomiting increases the pressure within the eye leading to blood vessels rupture.
Having dry eyes due to general dehydration, is a factor that adds to this occurrence (broken blood vessels of the eye).
If the symptoms don't improve after 3 days, and the eye redness doesn't subside within 2 weeks, see your physician.
It is good to know that some viruses that cause stomach flu, may also affect the eye conjunctiva.

Best wishes!
Marija