Love did not conquer anything or cure his insanity or his sickness etc.. Love was merely the catalyst for a self realization that allowed Rand to access his full potential as the Dragon Reborn. He was having a crisis of faith that kept him limited to simple human abilities. Rand is a Messianic figure and in a way was Reborn on Dragonmount for a 3rd time, this time his power is in his own "faith" rather than the more mundane OP strength.

Once he embraced the truth of being the DR he had access to a wide variety of, now uncorrupted, abilities. Note how he's now vastly stronger in the Power than anyone else rather than being on par with the strongest men. He seems to have some kind of direct control over his ta'veren effect and he is "one with the earth" in truth now, healing the corruption. I believe the same ability that drives Dark Friends insane is what is holding the madness at bay.