Ringworm is a fungal infection easily treated by a drugstores medicine. Ask the pharmacist. No worms involved at all. Although it is quite contagious highly unlikely it would be transferred through chlorinated water. Just don't share towels.
It is not advisable for an individual with ringworm to go for a swim. The condition is contagious and you may end up passing the infection to other swimmers. You may seek medical attention to get rid of the worms.