Answer:
Yes. It isn't a rash though it is from pressure when you throw up. It can appear as small purplish red freckles or groups of them. CPAP mask wearers sometimes get it because the blood cannot flow easily because of the mask pressure so it pools around the eyes. I can't find the proper medical spelling for it but it is pronounced
"pet-TIT-ee-ah". They are akin to broken capillaries. It will pass in a day or so. No worries. It is also a symptom found in a choking or strangulation.