Hi, I have just started to take my dd swimming, she is 7 months. I take her in the car seat and leave this by the pool side with a towel in for when she gets out. I wear my flip flops and leave these by the car seat, I'm very nervous about slipping with her.
I take two towels for her and one big one for me, get her dried and changed first then myself.
I have seen other mums take pushchairs and they leave them in the changing rooms.
I also take her changing mat with me, it squashes up into a carrier bag, its easier to get her changed on that on the floor rather than waiting for a changing table to be free (I take her to swimming lessons so there are lots of other babies there at the same time).
It was a bit faffy first couple of times, but we are use to it now, she loves it.
I'm sure you will have a great time.
p.s don't forget your pound for the locker.