I like this a lot. Feels vaguely like a Dowman Sayman comic.
The fish are a metaphor for social anxiety
I think that was just the case for the big carp that dislocated her jaw. When she confessed, it was a different species, whose Japanese pronunciation was a pun on "kissing" (plus, the fish literally kissed as well). It seems the various fish species represent different emotional states, social anxiety being just one of them. Note that she says people started avoiding her because of the fish vomiting, there are no indications she was a social outcast or that she was particularly anxious before this point.
I read it as a metaphor for being queer. Once she started vomiting fish, as in once she came out, people starting avoiding her. Tsucchi stays with her because vomiting fish, or being queer, doesn't bother her. Myaako thinks she might be cured of her fish vomiting, or queerness, if she kisses the person she likes. And in the end, it's not something that can be cured.
See also "Still Sick" for another work that compares queerness and sickness.
This is closer to my interpretation, but I also think social anxiety fits decently well. More generally, I think it works as a stand-in for anything about a person that causes them to be isolated from others.