Red Line Going Across Right Eye

Hello,
I was in the restroom and noticed that my right eye appears to have a red line going across it. I have only noticed this once before, several days ago. I didn't think anything of it because I thought it was just an eye irritation. Now I'm concerned. The capillaries in the middle of the eye as in..  where the "---" is, with the "o" being the iris.
I have never experienced this, and am concerned that my eyes have a worse problem? I wear glasses, but the eye doctor I went to in mid-August told me they were fine.
Is my right eye simply irritated? Did I rub it too hard?
All advice is greatly appreciated.
Thank you.

[John C Hagan III, MD, FACS, FAAO]

Can't tell from your descripition. If no pain, no pus, no reduced vision you can wait till Monday and see if it clears up. If not see your eye doctor.
JCH MD