The sexual counterpart is Homo-sexual. The two differ in that homo-romantic is the romantic attraction to only a gender the same as one's own. Homo-sexual is the sexual attraction to only a gender the same as one's own.
There may or may not be a sexual attraction for the gender that the Homo-romantic person is romantically attracted to.
A person can be homo-romantic but asexual, bisexual, heterosexual, homosexual, or pansexual.