Could my short chin be fixed with an implant or sliding genioplasty? (Photo)

Not sure if they meant by the short chin was relative to the height or the prominence. As you look at your pic in profile, your chin is retrusive (not far enough forward) but the overall height is good. The prominent point of your chin (called pogonion) is too close to your lip (too short) but in profile you have good face height. For you, a genioplasty would reorient the chin to make it more parallel with your jawline, increase the projection, and improve the support of your lower lip. It is always helpful to do a simulation so you can make sure you and your provider are seeing the same thing and speaking the same language. As your question highlights, sometimes surgeons speak their own language, which is a big part of why we do simulations for all of our patients, to make sure the focus is YOUR face and what fits best for you. And as an aside, you could do an implant as well, but I would highly recommend doing it from the outside (under chin), otherwise it will ride up toward your lip and make your chin look bunched up.

Chin augmentation
We usually make assessments based on standard pictures. Try using the timer on your camera or have someone else take the picture at straight angles from about 6 feet away. Pictures should basically look like mugshots. The person should look straightahead without facial expression.
Based on your pictures that you did show it looks like augmenting your chin would be a good option. Both implants and sliding genioplasty have advantages and disadvantages. You can talk to some local board-certified plastic surgeons and oral surgeons in your community about different procedure options. Chin augmentation can also be done with fillers.
Best,
Mats Hagstrom MD