The only pool I can remember is on the upper part of the city, near the northern wall. I may be wrong but you may be not too far from the school.

[And she's late to the party and never properly checks the network so, hey, say hello to someone who still doesn't know you're Steve's significant other. Rydia will be thrilled.]

Don't worry about Steve, he knows how to move around in the city. And if you don't feel safe... If I'm not wrong you should be able to reach the clinic in a few days of travel, there are supplies and other things there. And I shouldn't be too distant too, if you need help.
If I'm not wrong about your location, of course...