Romantic inclinations - in other words, you have a crush on someone, or you are currently or preparing to be in a relationship that is more than friends, or you are courting them, engaged to them, married to them, etcetera. Since it's Rin-san, I suppose it would actually more be "someone who you care for in a way that is not platonic, regardless of whether or not you would act upon that desire".

Is that a thorough enough definition for you, or would you like me to define "romantic" now as well?