An inverted V deformity occurs when the upper lateral cartilages collapse after osteotomies are done on the nasal bones to narrow the nose. This can be corrected with spreader grafts with cartilage from the nasal septum, ear or rib. This will correct the cosmetic deformity as well as open middle nasal vault to improve breathing. Good luck. Donald R. Nunn MD. Atlanta Plastic Surgeon
It is quite possible that you have collapse of yoru middle vault, Best to be seen in person to be properly evaluated.
You will benefit by consulting your plastic surgeon. Your breathing problem and appearance description suggest that reconstruction of your nasal internal valves may improve your situation.
It is impossible to answer this question without seeing photographs or doing an examination. Face forward and profile photos are preferred.