You are having a small bleed in your conjunctiva called subconjunctival hemorrhage
Are you awake of poking your eye during sleep or any fall of foreign body or any insect into eye?
Dont worry it will resolve in 7-10 days time
Please do cold compression twice a day with chilled water and clean cloth dipped in it.
Tablet limce 500 mg once daily for a week
Next Steps
if still persists
we need to do few blood tests like
complete blood picture,
bleeding time,
clotting time,
prothrombin time,
thrombin time,
activated partial thromboplatin time..