Honestly, I would continue with the swimming. My DS also got eczema as a baby that has improved as he has gotten older. We are also now able to ditch his special sensitive skin washes during the summer, but not winter.

He never had a flare up from the pool, but I was always religious about him and I having a shower together as soon as we got home from the pool so he would have a thorough rinse off then. (I could never be bothered carting all the paraphernalia to the pool...I would just put him in a dry nappy and a tracksuit, pull on my own tracksuit and go home and get ourselves sorted out there). Then I would moisturise him head to foot after the shower with Cetaphil lotion or Hydraderm pump pack (but we do this after every bath anyway, even now that he is 2yo).

Another little girl in the swimming class was also an eczema baby and her mum used to coat her in Cetaphil cream (the thicker stuff in the tub) before the lesson. I would imagine this made her a bit slippery to hold on to but I think her eczema was quite bad.

I would try a few more lessons, just making sure that afterwards your DD gets a thorough rinse off and you moisturise her skin with a good quality moisturiser, and see how you go. I know with my DS that as soon as we skip the moisturising for a few days his skin starts to flare up regardless of what we are using in his bath, so I'm a big believer in it.