How can I stop someone from constantly rubbing their eyes when they are infected?

Their eyes probably itch, why don't you try gently placing a cool or warm (which ever is more soothing to the person) washcloth on their eyes every once in awhile. this might help relieve some of the discomfort.
You can try placing soft mitts on their hands. Give them a box of tissues to hold and if they need to wipe their eyes they can use the tissue. Make sure that they wash their hands frequently to avoid spreading the infection. Antibiotics usually take between 24-48 hours to start working.