Is my jaw done growing? What's the best way to get a bigger longer jaw? (photo)

Women's jaw usually stop growing around 16.  Men's jaws will grow a little longer usually until 18, occasionally until 20 or 21.  If you no longer need bigger shoes, and are not getting taller, your jaw is probably done growing as well
The easiest way to get a bigger longer jaw is with a genioplasty or chin implant.  
Best of luck
Dr Rodman

The growth place in the mandible have usually closed by age 17 or 18 in a young man, so at 20 years of age, the mandible is probably fully matured and stopped growing.  Placement of a chin implant can augment the chin forward. Chin implants are manufactured in a large variety of sizes and shapes is best determined the time of the consultation and examination. For more information about chin implants, diagrams of the implants themselves and many before-and-after examples, please see the link and the video below

There are many ways to add to your chin, including a chin implant.  Chin implants can be made of temporary  fillers, or more permanently, using solid implants.  Both are safe.  Your jaw side/ angle can also be augmented.  The most common area to be augmented is in the chin area.  Using your picture I would consider a chin implant rather than a jawline modification procedure.

 Hi, I have performed many facial shaping procedures, including Chin Augmentation with dermal fillers or silastic chin implants, for over 30 years.  From the photo, your chin is quite weak.  The facial bones are done growing by the age of 13 to 15 years old, so at 20 years of age the chin won't grow anymore.   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".  
 The 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.  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.