Agree with others: ask to have a look at the pool facilities first and work out what you would do. I've gone to many different pools with toddlers on my own. usually, it's either: share a large changing room, or use the playpen in the communal one.
I put a slip over robe on the toddler, and give them a pack of raisins to eat (because biscuits crumble on the floor!)
If you get your hair wet, use a towelling cap or 'Buff' style tube to get your hair almost dry.
If you are able to use a car it's easy! This is what I do now:
We go pool ready, in towelling robes, and take a towel, toddler underwear, and 'pool shoes'. We look daft (who cares?). After swim, toddler costume off, underwear on and towelling robe. Me, quick towel over costume to get the drips off and pull on robe. Change shoes, straight out to the car, put the heater on! Proper change at home.