Go through these in order and stop at the first one that applies. If you are reading this for someone else, answer for them.
1
Is any of this happening now?
Call 911
Seek emergency care for a red or bloody-looking eye if you also have:
Sudden loss or major change of vision
Severe eye pain
A significant eye or head injury
A chemical splash or penetrating injury
Blood visible in front of the iris or pupil
New weakness, facial drooping, difficulty speaking, or a sudden severe headache
These features are not typical of a simple subconjunctival hemorrhage.
And for anyone, someone who:
is bleeding heavily and it will not stop with firm pressure
Other emergency signs, for anyone
Someone who is struggling to breathe, gasping, choking, or cannot get words out
Someone who has chest pain, tightness or pressure lasting more than a few minutes
Someone who has sudden weakness or drooping on one side of the face or body, slurred speech, or sudden confusion
Someone who is unconscious, or cannot be woken
Someone who has had a seizure that will not stop, or does not wake up afterwards
Someone who has lips or skin that look pale, blue, grey or blotchy
Someone who you believe has taken an overdose or swallowed something poisonous
2
Is any of this happening?
Be seen today
Obtain prompt, same-day advice if the redness comes with marked light sensitivity, increasing swelling, thick discharge, or moderate pain.
Contact lens wearers should be especially cautious about these symptoms because infections can worsen quickly.
3
Does any of this apply?
Book an appointment
Arrange a routine appointment if the blood has not begun to clear within two to three weeks, keeps returning, or affects both eyes.
You should also mention unexplained bruises, frequent nosebleeds, bleeding gums, or unusually heavy bleeding elsewhere.
The article also says
If you take a blood thinner, report repeated or extensive episodes to the professional managing that medicine.
Continue taking it unless you are specifically told otherwise.
Every sign above is quoted from the sofidex article on Subconjunctival hemorrhage. If you are not sure, err upward — it is always reasonable to be checked.