My 11 y.o. daughter didn't learn to swim until she was 8 after group lessons at five places since the age of four! I tried group, semi-private, and even private! What finally did it was a snorkling trip. After putting her face in the water with a snorkle mask, she was ready to hold her breath and add that to her dog paddling! Go figure.
Now my 4 y.o. son has had trouble feeling comfortable in group lessons since age 3 so we started with private ones. I think the only difference between him and the other kids is that, perhaps, I hadn't taken him to enough recreational swim time. Both of my kids are also pretty sensitive.
Our society is so focused on early mastery these days, without respect for kids and their needs. Whether it is readiness or a bad water experience, a young kid needs to feel secure in the water and lots of pools don't have a really shallow area for them. So they need to learn to play and love the water with someone they trust: you (or a trusted family member or friend)!
There are so many things we can do as parents that we don't try. I watch the swim teachers and the early stuff is not rocket science. You can do so much yourself and when your child is ready, then pass them on to the pro.
Your child and her fears are normal! Just build new and positive experiences this summer. Good luck.