I want to ask my coworker why she hasn't gotten a nose job
Is there a reason behind you wanting to ask your co-worker about her nose?
I hate people with ugly noses.
Do not tell her she has an ugly nose. That is very offensive and will hurt her self esteem. You need to be collaborative with your coworkers.
I needed to know because she looks like shit.
Keep those thoughts to yourself. There is no need to verbalize how you feel about her appearance to her, especially if it is negative.