Is there a way to fix my receding chin and deep labiomental fold? (Photo)

I suggest beginning with an in-person consultation to discuss your options. During your initial examination, your #chin will be evaluated along with the neck and jawline. A weak #chin implies a lack of chin support for the skin along the neck line. In younger individuals a chin implant alone is usually all that is needed to improve the appearance of the neck. Subsequently, it will also improve the overall #balance of the face and can create the illusion of a smaller nose. As a stand-alone procedure, chin augmentation can be performed in the office under local #anesthesia. For individuals with signs of #aging in the neck, a chin implant added to one of the recommended procedures above, will provide optimal results. Also, #liposuction under the chin is also another option your doctor can discuss. If you are not a candidate for chin or neck rejuvenation at the time of your #consultation, your board certified plastic surgeon can recommend alternatives to address your concern. 
However, there may be additional options to improve the appearance of your concern to improve the overall balance of your face. Such can be best evaluated in-person. Consulting with a board-certified plastic surgeon who specializes in #face, #neck and #chin procedures is important to ensure you are receiving the best advice, care, and surgical experience possible.

The forward projection of the chin can be brought forward by a sliding genioplasty or chin implant. Both chin augmentations, however, will make the labiomental crease deeper as that is fixed point that is not influenced by what happens to the bone beneath it. To help prevent it from becoming deeper it will need an additional treatment at the time of chin augmentation such as fat injections or an actual soft tissue implant.

A chin implant is designed to bring the chin forward and give added width, and a small amount of vertical height. Chin implants are not designed to help fix a deep  labiomental fold. Chin implants are manufactured in a variety of sizes and shapes, are composed of Silastic, and are inserted  through a sub mental approach under local anesthesia as an outpatient surgical procedure. For many examples and more information, please see link below

yes, the fold can be 'adjusted' based upon a few factors; including what the angulation of the lower incisors may be; and the chin height etc. In fact, it should always be considered critical in any genioplasty since it forms part of the 'curvature' of the profile.