I have red patches in my eyes but I feel no itching and pain?

Pinguecula. Often these patches are from sun damage or "elastotic degeneration" of the eyes. Try lubricating your eyes with artificial tears but if it bothers you and it does not improve, please see your ophthalmologist.
Could be many things. Red patches could be a few minor broken blood vessels from rubbing your eye-this occurs more frequently in the winter &in older patients. Red patches can also be benign growths of scar tissue at 3 and/or 9 o'clock on the eyeball where the white part (sclera) meets the shiny front part (cornea)-these are called pinguecula when they aren't on the cornea & pterygium when they are. See your eye doc!