Disclaimer: This answer is not a substitute for a consultation and examination. It refers to a diagnosis called 'subconjunctival haemorrhage', which may or may not apply in your case.
A 'subconjunctival haemorrhage' occurs when there is bleeding under the thin outer layer (conjunctiva) of the eye.
There are many possible causes, ranging from excessive straining, coughing, sneezing, to vigorous eye rubbing and getting hit or punched in the eye.
Sometimes, in the absence of any other known cause, factors such as dry eye and looseness of the conjunctiva (conjunctivochalasis) may also contribute to the condition by exacerbating the rubbing effect of the eyelid as it blinks over the conjunctiva.
If a person is taking blood thinning medications such as aspirin or easily bruises, and is getting bad subconjunctival haemorrhages, it may be worth consulting with their doctor to check on the dosage of their medication or the coagulation profile of their blood.
Having said all that, subconjunctival haemorrhages are usually harmless and get better on their own. There is no specific treatment for this condition, other than to look for possible contributing factors as mentioned above, and to treat them if present.
Probably the best thing to do is to see a doctor to have the diagnosis confirmed, and then take it from there.
