I don't want to go to prom with my girlfriend
Why wouldn't you go to prom with your girlfriend?
Her boobs are too big for her to wear the dress I chose
That is a superficial reason not to go to prom with her. You can suggest that she wears a shawl over her shoulders if it makes you that uncomfortable.
I'm not going with her if she wears a shawl over her shoulders.
Well it sounds like you aren't open to trying anything. Why did you pick her dress anyway, let her wear the dress she is comfortable in. You don't get to say what she wears to prom.