To get 220V, you need to use a 2-pole breaker which would connect to the Phase-A and B bus bars in your panel. If you only have single phase power to your pool panel, you won't be able to get 220V. If the wires are in conduit, you may be able to run all new wires, using the existing wires as a pull cord. I would remove the dead front on the panel and see how many wires are feeding the panel. Of course, take necessary precautions.
How would I tell whether I have single or dual phase power at the panel?
The power currently comes out of the house to a panel near the entrance to our pool. That houses the breakers for an outlet there, the pool light, and the breaker for power running out to the panel by the pumps.