Okay so I Googled "sickgender" and the first thing that comes up is a Pinterest thing with a different flag & definition but it doesn't take me to the post when I click, and the archive is blank, so that seems inaccessible, though I think we could still use it because the definition & flag come up on the Google search. I also found another Tumblr gender named "sickgender" with /another/ definition. Long story short the name has been used before so you might want to pick a different name :)
Tumblr one
Pinterest one:
(Also just want to say since it seems like the next obvious name choice - "gendersick" has already been coined too. Based on Latin words for "sick" you /could/ user: aegergender, infirmugender, causariugender. Just ideas.)