I've watched Korean and Japanese dramas pretty regularly (and by "pretty regularly" I mean almost every day). I don't follow contemporary music at all, not from Japan or South Korea or from anywhere else in the world. I don't actively seek new information about K/J artists or celebrities, either.
I think I can understand where OP's coming from, though, about the feeling of wanting to keep yourself informed on all aspects of this particular thing that you're really into (in OP's case, East Asian dramas, I guess) because I was like that too, at one time. I think I just accepted as I got older that it's impossible to keep up with the latest in pop culture, and I'm fine with that.