You have a condition called retrognathia in which your chin is small or set back and the skin of your neck recedes as a result giving you a double chin look.  While two syringes of any filler will help, 2 cc of added volume is not very much. Here is a video that shows you just how little is in each syringe.  In my experience at least 4 or 5 syringes are required to get any noticeable result.  If you do decide that filler is best for you then I recommend Bellafill since you will not have to keep going back to be refilled every couple of years.
The best option for you would be a chin implant. This would bring your upper neck skin or under your chin skin out and give you the profile that you want.
Here is a link to before and after photos of a patient with a similar problem to yours who had a chin implant placed.
This is a very simple operation and can be done under local anesthesia.