Hi there. It might be worth trying a lip flip first as the results only last roughly 2 months. The product wears off faster here than higher areas of the face (3-4 months) due to the frequency and intensity of movement of the muscles around the mouth which help us to talk and chew. So if you...
Yes, it can. This problem can arise with the activation of your depressor septi nasalis muscles below your nose. When they activate with certain activities like smiling, this can pull the tip of your nose down. This can be treated with botox or surgically with the removal of the muscle.
Botox can help restore symmetry to an otherwise asymmetric face. Although, the issue is often a hyperactive muscle and in your particular case it sounds like the depressor anguli oris muscle. Targeting this muscle with Botox can deactivate the muscle and help give you the look that you want.