This sounds like what is called a subconjunctival hemorrhage.
This essentially amounts to a bruise on the eye, except on the eye the tissue that the blood is underneath is transparent so you see the blood exactly the color it is, versus a bruise on your arm which is hiding beneath layers of skin.
There are things that can predispose to getting these hemorrhages. Taking aspirin, ibuprofen, motrin, aleve, naprosyn can thin the blood and predispose to these. Also taking garlic, ginseng, ginko biloba and vitamen E can also thin the blood and predispose to getting these.
Also when there is significant pressure being generated in the eye or head, this can happen from that. Examples of this include eye rubbing, sneezing, coughing, lifting a heavy load or straining against a bowel movement.
If you are not taking any of these medicines or vitamins and/or you've not had any of these pressure causing events, then having multiple episodes of this could be a sign of a bleeding problem and should be checked out by your primary care doctor.
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