Is my labiomental fold too deep for a chin implant? (photos)

One of the interesting features of chin implants versus genioplasty is that they tend to build slightly the labiomental crease. In your situation the crease has modest visibility and I believe that the advice you have received is correct and a chin implant would be a suitable approach.

By definition any form of chin augmentation is going to make the labiomental fold deeper since it is a fixed anatomic point. No one's labiomental fold is too deep for chin augmentation as it lies above the chin bone. Whether you will see a deepened labiomental fold as an undesirable tradeoff for more chin projection is the question.

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  From the photos, your chin is a bit weak and the mental groove within average limits.  When the chin is weak, this creates an imbalance making the nose appear larger, the mid face top heavy, the lower face looks short, de-emphasizes the lips and allows early formation of a "double chin".  
 Proper placement of a silastic chin implant adds forward projection to the chin thereby creating harmony and balance to the lower face.  Using the same incision, liposuction can be performed to reduce the fat and further shape the neck.  Excess skin, from below the chin, can also be removed through the same incision.  
 I have found that placement of a silastic chin implant, through a small curved incision under the chin (also allows excess skin removal) to be very safe, quick, highly effective and far less invasive than a sliding genioplasty (requires extensive tissue dissection, bone cuts and placement of metal screws and plates to secure the cut segments of bone).  I perform chin implant surgery in 30 minutes or less, often using a local anesthetic alone.  In my opinion, you are a good candidate for chin implant surgery.  
Hope this helps.