I have a Bagged Swordtail Fish and it gives me the option to find it a home. When I go there it tells me I home nowhere to put it. Is there something I have to have in order to free it?

you can put it into an [item2=empty aquarium] and it can then be a Minion. It isn't actually freed like a Snow Fairy is.

Thank you! I figured there was some sort of Aquarium, but I couldn't find anything. :) Is it possible to view it with the fish inside?

Yup, each type of fish makes a specific aquarium item.