I don't think that many girls go by
Jessie. All the girls named
Jessica that I've known have either gone by
Jessica, or casually gone by
Jess. I only know one female
Jessie, and that's her full name.
Jesse is quite a handsome name for a boy, though not my style, imo. Looking at popularity data, it has never left the top 200, and 2013 is the first year it had left the top 150. Especially spelled
Jesse, I doubt anyone would immediately assume he was a girl.