I understand that "do" is used for emphasis here, but why did she say "do I feel bad" instead of "I do feel bad" even though it is not a question?
Good question! "Boy do I" is an expression that is used to mean "I really" but add emphasis and make it sound more dramatic. "Do" is placed before "I" in this expression to set it up as if the speaker is asking a question, although they are really telling a statement. This question-like statement is used to add emphasis and express sincerity. Ex: Boy do I look good in this outfit! Ex: Boy am I happy you're here!