Frodo, is not in love with Gollum, he feels sorry for him because he thinks that he will become like him if he fails to destroy The Ring. As he says in he needs to believe that there is hope for Smeagol (y'all don't call him Gollum, that is just plain mean) to get to be normall again, so that he can believe that The ring will not take over his soul. Frodo's only love by the end of both book and movie will be the Ring, even if it'll be destroyed he'll still love it. That is why he will never get married, The Ring took a place in his heart that no woman could replace.
Elen sila lumenn omentilmo,
Cormamin niuve tenna' ta elea lle au',
Amin mela lle.