You have traumatic sub conjunctival hemorrhage( localized collection of blood between the conjunctival tissue layers). This doesn't need to be drained as it wil get absorbed within 2-3wks time. If it is causing irritation ,while blinkng,use a lubricant eyedrops 4 times a day to comfort you.
If you have pain on moving the eyes with glare and defective vision,then consult an ophthalmologist at the earliest as trauma must have caused Intra ocular inflammation
and hence a detailed examination.cold
compresses does help a little.
Take care :-).