'Love you crazily' would technically be correct, but native speakers usually don't say that.

'Love you crazy' is a catchy song title, but it makes no sense grammatically. 'Love you crazily' fits English grammar rules, but it still doesn't mean very much. It isn't something natives speakers would say. In general, you should be careful about trying to learn grammar from songs. Songs often make their own rules, according to what fits the music and or according to what sounds fun and catchy. In fact, song writers often deliberately break the rules of grammar or use odd-sounding phrases just for fun, or to make the song more memorable.

i love you crazily seems correct to me but i am not sure