You are referring to a slightly convex facial profile which looks aesthetically better on a female than a male. This can be improved by chin augmentation using either an implant or a sliding genioplasty. There are advantages and disadvantages with either technique.
It does appear that you have a recessed chin and some excess fatty tissue under your chin/ jaw. A chin implant will help improve your profile by projecting your chin and it will also stretch the tissue under your chin as well creating a small amount of improvement in your neck. The best result...
You are incorrect in assuming that chin augmentation would not improve your neck angle. A chin implant will not but a sliding genioplasty will as it pulls the muscles and skin under the chin forward. With your degree of horizontal chin shortness, a sliding genioplasty would be the best chin...