Final Results of Submental Liposuction?

The way you look right after submental liposuction is a good indicator of how you will look. You just have to be patient.
After liposuction, your body starts forming adhesions from the skin flap to the underlying tissues. These adhesions are a form of scar tissue, and the problem is that they obstruct the drainage of fluids thru the lymphatics. As this scar tissue resolves and lymphatic channels reestablish, the fluid is more easily evacuated and swelling disappears.
At this point, compression is the best answer as it squeezes the fluids out and helps the scar tissue remodel.
You can read a little bit more about compression at the link below

Generally, final results appear in about three to four months after surgery. You may be experiencing swelling that still needs to subside. 

Usually as the more you do physically, the more swelling sets in. The best thing to do is what you are doing is wearing the neck strap as much as possible. It usually takes about 4 months before your final result is apparent.
So be patient and continue with the strap and see how things shape up in the coming months.
Good luck.