"Mouth" (la boca) includes more than just one's lips ("los labios").
I thought that when referring to parts of the body spanish doesn't use "mi" but "el" or "la" so why couldn't "la boca" translate as "my mouth"?
Don't overvalue that rule. You only have the option to not use mi or any possessive marker if it's clear whose mouth it is. I.e. if the person having that body part has been mentioned before. Consider:
- Tengo comida en la/mi boca. - I have food in (the)/my mouth. It's clear that the sentence is about 'me', so I don't need to use the possessive. But I can.
- Hay comida en mi boca. - There is food in my mouth. No mentioning of a person, so I have to state exactly whose mouth I am talking about.