Your pain may or may not be related to your implant. Late infections can and do occur, but without any swelling, erythema, fever or other symptoms it doesn't sound like an infection. Implants can get infected via hematogenous (blood borne) spread from other infections like you've suggested such as a sinus infection. Other sites of infection, even ones far from the implant, such as infected cuts on the hands or legs or pelvic inflammatory disease could lead to blood borne bacteria that could infect an implant.
Your symptoms sound more like an issue with the mental nerve which runs right near your implant. It's odd for an implant to move after so many years, but they can. Implants can also cause bone resorption that may lead to "movement" of the implant. You should get at least a tentative diagnosis before you begin treatment.
I'm not sure from your question whether your physician has suggested fat injections to treat your pain or has suggested removing the implant and then putting in fat. Fat injections are not a solution for pain. Find out what's causing the pain first and treat it.
It could very much be infection. In that case, the implant need to be removed and treated for infefction based on cultures. It could be capsular contracture, and your implant needs revision.
Do not blame yourself, you have not done anything. You need an experienced PS
Rule out delayed complication
By the history you have given there are two main probable diagnoses that need to be addressed; infection and bone erosion. Most of this can be seen or figured out with an examination. A plain film X-ray can also help and is not very expensive.
Some types of implants are more likely to cause these complications in the delayed time period. Have these issues looked at and I think you will be on your way to getting things fixed.
Dealyed pain after an implant
Pain and soreness can be related to your implant, and a possible current infection, or it can be a totally unrelated problem. Once you have an implant, it is a foreign body, and it is possible to develop an infection around it later in life, sometimes many years later.
In any case, fat injections are not the answer to treating pain. I would be extremely skeptical of this procedure in your case, and I would certainly want to investigate further what is causing your problem. If your treating physician is not able to diagnose it, perhaps he or she can refer you to another physician who can diagnose and treat it.
Chin Implant Pain Warrants Examination
I would most certainly speak with the surgeon who performed your implantation. Unfortunately there is always a risk of infection with a foreign body such as a chin implant at any point in time. If infected, you may need long term antibiotics or removal of the implant.
Numbness and pain after chin implantation - chin implants
Any acute change associated with an implant warrants evaluation and emergent management. Since there is a nerve associated in proximity of the implant, I would advise you to consult with your plastic surgeon to discuss immediately.
Pain years after chin implant
Pain and tingling years after a chin implant could mean a number of things:
1. The implant is pressing against your nerve which can cause pain, tingling, and numbness
2. There may have been trauma (injury) to the jaw shifting the implant
3. There may be an infection
5 weeks of pain with an implant, is worrisome for an infection, despite your lack of signs. An infection must be ruled out, and this may include blood work, X-rays, CT, or even MRI.
Chin implants have been reported to cause dental injuries, and so a dental visit may be in order as well.
I would not have any additional surgery until the chin/implant is given a clean bill of health.