rub at (something)
To exert pressure on and move in contact with something. Make sure not to rub at your eye if you've got something in there—it will only make it more irritated. He rubbed at the coin with a cloth to make it shine a bit brighter.
rub (away) at something
to chafe or scrape something, repeatedly. The side of his shoe rubbed away at the side of his desk until the paint wore off. Don't rub at your sore. It will get worse.