Is 承認 appropriate when describing the following situation? I've known a girl a while and she recently confessed that she liked me. I know "承認" is used for admitting that you have committed a crime or done something else wrong, but liking someone isn't wrong. I imagined Chinese would have a more nuanced word for this situation.
承认 means 'to admit'. It isn't only used when the deed being admitted is wrong or illegal. It can be shameful, embarrassing or simply too shy to admit, which I believe is the situation in your example.
Although 承认 is fine to use, I think an even better word is 坦白, which means 'to confess'. Just like the English word (and like 承认), it's commonly used for sins or guilt, but it can be used for embarrassment or shyness as well.
We confessed that we like each other.