Should I lose weight?

Hi, so I never thought I was fat. I'm 5'7",21yrs old and I weigh 120lbs. I wear XS(extra small) or size 1 or 2,depending on the brands. I always thought I looked good,happy with my body,not fat at all. My boyfriend I've been seeing for a couple of months,he sometimes grabs my stomach and says I need to eat less,jokingly but it hurts because he almost says it every time we snuggle and I just don't feel good about myself. I have a small butt, which he says is cute because he likes small butts but the other day we were outside and he saw this girl with a small butt which he complimented and told me I need to do butt crunches to get a supermodel tight butt. It made me feel horrible but I didn't tell him that. Now I absolutely hate myself every time I look in the mirror. I feel ugly. I skip meals and whenever hunger gets too much and I eat I feel guilty and like a fat cow. I feel like I disappoint him.

Am I really fat? How much weight should I lose? Would really appreciate any answers.
Should I lose weight?
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