承認 for confessing admiration
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.
我们坦白了彼此喜欢对方。