I didn't notice her self pleasure scenes were associated
with the water. But I should have noticed the three scars
on her neck being gills since the monster didn't change them
to something they're not. He just healed them.

Though she still may not be mermaid. A second viewing
maybe in order.

I didn't realise the mermaid association wasn't a widely held understanding/thought. As you say- she got a lot of 'pleasure' in water and knew exactly when it would rain. Furthermore, (just like Aerial) mermaids are not traditionally able to speak.

Huh? she was supposed to be a mermaid? that was not obvious

Well, that was the way I looked at it. Looking online it seems there's some support for that idea. I like that sort of film- you need to think a bit and the answers aren't black and white but are open to interpretation.
One of my favourite films is Mulholland Drive- just because every single scene and every line of dialogue is meaningful and can be interpreted in different ways.

Edit: PS- sorry to take over this thread and probably should have spoilers...
Just read actress Sally Hawkins had the idea for a character who didnt know she was a mermaid. Del Toro liked the idea and asked her if he could use the idea in this film. Thus, I'm not sure the story started out like that but developed over the course of production.
PPS- Sally Hawkins is brilliant in a small UK film called 'Made in Dagenham'- I recommend it.