I have a deviated septum, and I'm wondering if that contributes to my crooked mouth and drooping eyelid? (photo)

Thank you for providing both a frontal, and a profile view of your nose. The entire body, including the face is asymmetric. Embryologically, we are formed as humans by neural tubes. Therefore, our bodies-- are two bodies fused in the middle. No human being is symmetric. there is no operation that i know of that will make one side of the body completely and thoroughly match the other.Improving your nose will greatly enhance your overall appearance, straightening your septum will improve your breathing, but not affect your mouth or droopy eye. Blepharoplasty may improve the eyelid asymmetry but you need to be fully examined further.

A deviated septum has nothing to do with a crooked mouth and a drooping eyelid. Repairing a deviated septum will simply improve airflow through the nose and not change the shape of the nose. To repair a crooked nose, medial and lateral osteotomies of the nasal bones along with a spreader graft placement underneath the concave upper lateral cartilage will be required.  All this can be accomplished with a closed rhinoplasty approach with all incisions placed on the inside of the nose. For many examples please see the link  And the video below

DNS do not contribute to droopy mouth and eyelid. Have you ever had a Bell's Palsy? See a facial plastic surgeon to assess your asymmetry and facial movement.