From what I remember (I'm due for a re-watch before S2), after she died, she wasn't really mourned by the other students/community and just forgotten about. That's when fans started the Justice for Barb rallying cry. Anyone can correct me if I'm wrong. I definitely think the Emmy nod was influenced by the attention she got online. Edit: Also I think due to societal norms and entertainment tropes, Barb was the "nerd" yet it's the attractive teens that survived.
I had the same experience. Didn't watch the show until a few months after it aired, and I was totally baffled. She legitimately has like 8 lines in the whole show.
I will say this about Barb. I watched Stranger Things before the Barb phenomenon happened and I can't say I didn't think about her character a lot afterward. She was the only borderline major character who actually died and Eleven discovering her body and screaming "Gone!" was one of the most haunting moments of the show. So when it wasn't mentioned again after that, it made everything surrounding her character feel darker and more unsettling. Not enough to generate an Emmy nomination and a thousand Buzzfeed articles, but still.
Wow yeah let's give an award to the corpse instead of the girl who reacted to it in an amazing way Fuck Barb, Millie deserves every award, she makes this show
Only one should win and only one should have been nominated. If you give nomination spots to memes the award loses some prestige anyway.
Awards shows are kind of silly anyway. While I think nominating Barb's actress is super silly, there's also no reason to be that upset about it.