This is likely a metaphorical and jocular expression, using the noun "nez/nose" for subtle word-play.
The entire sentence means something along the lines of:
She's usually nice and kind, but just lets trivial things get up her nose {= quick to lose her temper}. Not to imply, of course, that she doesn't have a pretty nose!
1: les épices lui montent facilement au nez
Literally: spices can all too easily go up her nose
{Or more like: = get up her nose = little things can irritate her}
2: qu'elle a (un) joli (nez) d'ailleurs !
The noun "nez" is omitted here, which necessitates the use of the verb "avoir".