Will my Results Improve 3 Weeks After Chin Lipo and Chin Implant?

Extreme tightness is extremely common 3 weeks following agressive chin liposuction. However, the other symptoms of numbness and difficulty moving are less common. You should discuss these concerns with the surgeon so that he/she can review these issues.

There will be some stiffness and woodiness in the neck until all edema and fibrosis settles down in the healing process. A neck strap will not help since it has been three weeks after surgery. Try to be patient; it is going to take time to for all of this to settle down. We expect some degree of numbness after this type of surgery to last approximately two to three months.

Not seeing before and current pictures and not knowing the exact techniques performed, it is very difficult to comment on your results. Nevertheless, three weeks is too soon to accurately judge your ultimate results. In my experience, the contour of the neck will improve over several months following liposuction (especially if there is no appreciable weight gain). Swelling, tightness, numbness are not uncommon within the first several weeks following the procedures that you had performed.

The tight feeling is very common, and will resolve in few weeks. There is a possibility that you are swallen and will see more improvement with time. I would wait 12 weeks.
As for the numbness the surgery can cause some numbness which resolves faily quickly. If there is no improvement in the next few weeks, the implant may be causing pressure on the MENTAL nerve causing the numbness. in that case i would remove the implant. It is very rare that the injury to the nerve is permanent.
As for the movement of the lip this is another nerve that supplies the muscles that move the lip. It could be not working due to the surgical trauma, like swelling, in that case it will come back. if the muscles or the nerve in injured it may not come back completely.
The best is to discuss your concerns with your Plastic Surgeon who can give you a better explanations and diagnosis.

3 weeks is far too early to evaluate the results of Chin Implant and Chin Liposuction. Wearing your chin strap or chin compression garment should help improve your results.

Numbness and stiff chin are common after Chin Implant and definitely should improve.

If your lips are also numb you should check with your doctor. Numbness of the lips can occur after Chin Implant surgery but should get better between 3-6 weeks. Occasionally nerve injury can occur during Chin Implant surgery, but lip numbness is usually temporary and resolves by 6 weeks

You are 3 weeks post op, so many of these findings are not fully unexpected.  Swelling is still present, contraction of the skin has not onset, surgical insult is barely healed. Numbness from the placement of the implant or even the liposuction is a finding that should resolve. Contracture following liposuction is maximal at 6 months. If your skin does not contract enough, you may consider having some skin removed as well, but wait 6 months.
Yes, wear the chin strap as much as possible, this will reduce the swelling for up to 3 months. If you notice onset of swelling when you take the strap off, it is not time to stop wearing it. If there is not change, the strap is no longer helping with swelling. The more uniform the compression and the better you alleviate the swelling the better the ultimate result. Don't worry too much right now, but continue close follow up with your doctor to get the reassurance you need and address the problems if they persist longer than 6 months. 
Best Wishes!