I am also very afraid of fish, I don't care how much bigger I am or how they are more afraid of me,
I am afraid of fish!
That said, we did Discovery Cove a few years ago and I loved the dolphin swim part and the lazy river. Swimming with the dolphin was different for me because it was larger and couldn't sneak up by my feet. The trainers keep a very close watch on your dolphin and ease you into the swimming with it part. It truly is an amazing experience!
Snorkeling in the fish area though was a totally different experience, did you know you can scream through a snorkel? I also found out that I am not able to walk on DH's back while he is swimming... he kept mumbling something about drowning him, it was hard to tell as I held him under water.
I will also admit to this, I used my children as a shield

They loved the ray pool and wanted to cut back through it to get to our chairs... I wanted to walk around. They told me they would walk one on each side of me and protect me if I did it. DH walked behind me. Someone pinched me and I let out a scream heard across the park, and it wasn't a muffled one like in the snorkel
So, point to my post - go swim with the dolphins, it is amazing! Skip the fish area and enjoy the lazy river instead.