The blood vessels in your eyes are very fine and delicate.
Blood thinners can cause this, excessive exercise, coughing, pushing, or nothing at all can cause them.
It will look a little worse as it starts to go away. Your eye could take on a green/yellow appearance in that area.
It's called a Subconjunctival Hemhorrage and is very common. We see them all the time. I have seen them before where it will actucally swell and drape over the lid. So the person has this red 'gel' coming out of their eye. As you can imagine, they freak out but there is nothing that needs to be done. Only time.