From the history provided, it seems that your friend is having red and bruised eyes following vomiting. This is probably because of rupture of very small blood vessels in the eyelids during vomiting.
This will not require any treatment and it will subside in one or two weeks, as the blood gets reabsorbed. Hence, you need not have to worry about this. Applying cold compression over the eyelids will provide symptomatic relief.
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