Sometimes, you would feel uncomfortable to cause repeated vomiting, which would build up muscular tension, especially the stomach muscle. At the same time, it would increase intra-cranial pressure immediately, that is to say, the blood pressure could be increased due to the muscle movement. And the chronic pressure on the eyes could cause pain normally. However, you have to go to see eye doctor if the redness and pain lasts for a long period because it could cause macular degeneration as well.
The problem you describe is called a subconjunctival haemorrhage and it's completely harmless.It will disappear in a couple of weeks and doesn't require any medical treatment.The haemorrhage is caused by an increase in pressure in the abdominal cavity that spreads to the blood vessels and causes the tiny vessels in the mucous membrane of the eye to burst.This is why the condition typically occurs in connection with coughing or vomiting.
The vomiting will cause head congestion even eye congestion, especially severe vomiting after drinking, so the eyes turn red and get distending pain. The pressure within your head will be increased after vomiting, which causes the blood capillary ruptured around your eyes. It's not a big issue just take some relax, you'll be well after a while.
Headache and eye pain after vomiting are the same with the symptoms of intracranial pressure increasing. But I still suggest that you go to a hospital to do a further inspection, such as craniocerebral magnetic resonance, retinal edema, cerebrospinal fluid pressure and so on. At the same time, you can use mannitol to reduce intracranial pressure and see if the symptoms can be mitigated.
Firstly you have to figure out what you have done recently, have you been drinking? Or have you been doing something unusual? As a matter of fact, eye pain is a sign of demand for rest of your eyes. Maybe it is because your eye pressure is too high, which is resulted from drinking alcohol. So you can just take it easy, drink some hot water, and get some real good sleep, maybe you will be alright the following morning!