My mouth is not relaxed when it is closed. Should I get chin surgery? (Photo)

Thank you for your pictures.  In my opinion, I would recommend a sliding genioplasty to improve your facial profile.  
     This will provide you a natural result because I use your own tissue (bone) to improve your profile. For over 26 years I have performed sliding genioplasties and in my opinion it is the most natural and stable form of chin enhancement. A sliding genioplasty IS VERSATILE.  This technique can be use increase the prominence of the chin, decrease the prominence of the chin and it even can be used to correct asymmetries.  Chin enhancement can be performed using soft solid medical grade silicone implants.  This technique is a good technique but lacks the versatility of a sliding genioplasty.  A chin implant can ONLY be used to increase the prominence of the chin.
    The procedure is performed as an outpatient procedure. General anesthetic is required. The procedure typically consists of improving the chin position and contour through an incision inside the mouth . This incision is completely hidden.  This allows access to the bony chin.  An incision (osteotomy) is made in the bony chin to separate it from the lower jaw.  This segment of chin can be positioned as needed (forward, backward and/or to the left or right) to produce the desired result.  The chin is fixed in its new position with either titanium screws or stainless steel wires.  The metals are very kind to the body.  The incision is carefully closed to reposition the muscle of the chin and lower lip with dissolvable stitches.  Very light compression tape is placed to help manage swelling.  A sliding genioplasty can be performed with liposuction of neck to further enhance contour and profile.  A liquid diet is required for 48 hours then a soft diet is recommended for 10 days.  Typically, the first appointment after surgery is typically in 48-72 hours.
     Remember if you're considering chin enhancement it is always wise to consult with a board certified plastic surgeon that has experience with maxillofacial surgery techniques.  Best wishes.

You have lower lip incompetence and a mentalis muscle strain which are classic indications for a sliding genioplasty chin advancement procedure. Your chin is both horizontally short and vertically long. A sliding genioplasty brings the chin forward while vertically shortening it which you need.

Your photos show a recessive chin.  Your profile should be in a straight plane, and yours is not.  Chin Implant surgery would be a good option for you.  See a board certified plastic surgeon for an in person evaluation.