Most subconjunctival hemorrhages are not dangerous and resolve on their own within a few weeks but if not then you should see an eye doctor or go to urgent care.
Bleeding that happens under the conjunctiva is not a dangerous condition and usually requires no treatment and it's usually caused by high blood pressure or stress that causes the blood vessel in your eye to pop.
I've had a subconjunctival hemorrhage a few years ago and it went away on it's own within 2 weeks and didn't require any treatment.