My cat is missing a patch of fur..

i recently noticed a patch of fur missing on my cats upper back. it
seems like it would be on her shoulder. she's been vomitting on and
off, some days worse than others. i'm going to be taking to her to a
vet tomorrow but i'm wondering if maybe anyone has any suggestions to
what it could be. she's seven years old. i was thinking possibly
anxiety since i had just moved out of my parents house and started
roommating. my roommate has 3 other cats, which my cat is used to from
living with cats her whole life. the only difference is that i try to
keep her in my bedroom all the time since i've noticed she doesn't like
any other cats using her litter box and will stop using it. so i was
thinking it could possibly be a case of being homesick and pulling her
fur out. but i'm not sure if she could reach to even be able to. and,
i've never noticed her pulling any fur.