Your wide tip and nasal base can be reduced with rhinoplasty surgery. You describe very soft cartilages; your inverted V deformity with a narrow mid-nose and the deep alar creases can be improved with cartilage grafts.
A rhinoplasty and breast augmentation can be performed at the same time with one recovery period. The rhinoplasty procedure is technically the more difficult one, so choose your rhinoplasty surgeon very wisely. Digital computer imaging will be helpful in understanding what can be a...
Trauma to the cartilage is more difficult to manage than bone. Bone can usually be reset or "popped" out into position. Your siutuation sounds as if the cartilage tore loose from the nasal bones, causing them to collapse. The repair usually requires suturing and spreader grafts...