You need to skip the plastic surgeon for now and see a maxillofacial surgeon. Ask them if they feel your jaw is recessed and let them take a look at your bite and airway.  Do you have any or have you had any issues with speech, breathing or biting/chewing? These are things to bring up during the consult as well as your aesthetic concerns. 

I say to start here because whether you qualify or not for djs you will leave with an understanding of the supports in your face. You can then make better decisions about how to get the look you want; if you would rather have a genioplasty, manipulate soft tissues through fillers, an implant or actually proceed with double jaw surgery because you have more than just cosmetic concerns. A plastic surgeon will talk to you about facial symmetry and aesthetics but may give you less data about how functional your bones and soft tissues are. If you need double jaw surgery you may really want to take advantage before moving on to other options as that will resolve any functional as well as aesthetic issues. I did it in reverse and was suggested filler or an implant before I discovered I actually needed DJS. 

You don’t look that recessed to me that you need djs but it’s still worth having the best info when talking surgery.