Question
I noticed at the end of the day a red spot on the outer part of my eye near the iris. The next morning it had turned into a line mimicking the curve of, and next to the iris. Now the line, 3 days later, seems longer and still following the curve of my iris. A couple of years ago I got some tent waterproofing in my eye and it looks exactly the same as that did in the same place.
Answer
I am going to guess and say that the similarity to the tent waterproofing in your eye to what you are experiencing now is coincidental. What you describe MAY be just a subconjunctival hemorrhage. This is a broken blood vessel between the white part of the eye and the clear skin (conjunctiva) that covers it. Often it starts out smaller and then spreads out. There is usually a line of white between the red part and the colored part of the eye. If it is a subconjunctival hemorrhage, there will be no pain, the vision will not be affected, and the redness will begin to turn brownish within a few days and then fade, sometimes to yellow before going away completely. These are not serious unless they keep recurring, in which case they could be a sign of some general health problem like high blood pressure. They are usually caused by coughing, sneezing or carrying something too heavy.
If what I just described does not match exactly what you have going on, you must see an eye doctor to find out what it is.