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Do you remember what any of the characters looked like? Was the main character a boy or girl? Off the top of my head, I know that Nana has been on Netflix, and it features romantic subplots and a character in a punk rock band.
EDIT: I didn't think of it before because I figured you would've mentioned if it was a same-sex romance and I didn't think the show had been on Netflix, but from your description it could also be Gravitation.
Edited by livewithstyle
That does sound like Gravitation.
there was this one show that was on netflix that had a love story in it and it had to do with a band, maybe a boy band, but now its off netflix and i cant rember it