End of problem. It probably was a small hemorrhage in a capillary vessel
It is on the side near the nose, in the very corner. I noticed on the other eye, there is no red dot but the caruncle if that is what it's called, is kind of swollen. I do have a problem with dry eye. Could that cause either of these things?
If its in the side of your eye near your nose it likely is the "caruncle" if in the very corner. If on your eyelid it could be the eyelid puncta or opening of the tear duct (one on upper and one on lower) If its on the side towards the ear can't offer any useful information. Use a search engine and pull up pictures of the "lacrimal caruncle" and see if that is what you're noticing. JCH MD