Sorry didnt mean to double post!
A spontaneious subconjunctival hemorrahge is very common and usually totally harmless and usually in one eye. If it both eyes at the same time it might be more likely to be related to trauma, severe coughing or vomiting, blood disorders that make the blood too thim, bleeding in the orbits, or blood way too think from warfarin or thinning medications.
JCH MD
Thanks for the reply, glad to hear it's most likely irrelevant.