Red eyes means there is inflammation in the eye and can be caused by a variety of things including conjuctivitis, blepahritis, keratitis, uveitis, glaucoma to name a few. Some of these diseases can be serious and can cause blindness so i would recommend an exam by your vet to determine the exact cause and appropriate treatment. Your vet may need to do some diagnostic tests to determine the exact cause. Is she rubbing at her eyes, do you see a discharge, is she squinting at all, does she seem painful at all, or does she have a history of any allergies?
The fact that she is anorexic and vomited twice is also concerning as some systemic diseases can cause inflammation in the eyes and redness. Things like diabetes, high blood pressure, pancreatitis, lyme disease, viruses, bacteria, and tumors.
Below are some website that may be helpful.
Please let me know if you have any questions.