Injections into the nose are NOT recommended
As a rhinoplasty and facial rejuvenation specialist, I have seen many more problems with dermal fillers injected into the nose than I have good long term results. Therefore, I strongly suggest patients do not seek the quick injectable fix or risk significant long term nose problems including inflammatory nodules, scarring, redness, pain, nasal skin changes, and nasal deformity.
Removal of an injected material is very difficult, but sometimes possible if the material is located in the layer between the skin of the nose and its underlying structure. In your case, it sounds like the Radiesse has caused an inflammatory reaction around your nostrils. Steroid injections around the nostrils could actually cause further deformity and are not recommended. Oral streoids may help temporarily, but might not help over the long haul. Further massage is not recommended for fear the Radiesse may spread even further. Have you tried a course of antibiotics?
Radiesse has been touted to last up to 18 months, so you could ride it out and hope for the best. Another thought is a full thickness punch biopsy to see if there is a giant cell foreign body reaction with polarizing material. This might confirm that the cause is the Radiesse. Sorry I'm not more help, but these are a few thoughts!
Radiesse itself does not cause reactions like you describe. However, if sterile technique was not followed, you may have a superficial injection is very unusual. You should make sure you follow closely with your doctor. I cannot stress enough that you should make sure you are injected by a board certified plastic surgeon and not in some spa or salon where they are more casual about issues such as sterility.
Hyaluronic acid filler more appropriate for nose augmentation
Filler injection for the nose can be a tricky proposition as the material can easily move even if injected in perfectly placed plane underneath the muscle. Hyaluronic acid filler is advisable for nasal augmentation given the fact the material can be completely reversed with hyaluronidase whereas if you have problem with Radiesse, you are stuck with it for potentially several months.
Radiesse nose jobs are very safe
Unlike Dr. Capone, I have done many nose augmentations with Radiesse and have never had a problem, nor seen any in my practice. I have seen problems from surgical nose jobs however and have corrected quite a few (cosmetically) using fillers.
I have never heard of an allergic reaction to Radiesse. Your problem sounds as if it might not be related to Radiesse since it has been 3 years and the product should have dissolved by now. Also, it seems unlikely that Radiesse could be massaged into the nostril area from another area of your nose. Radiesse can be smoothed out with massage but not moved around, especially in an area such as the nose where the skin is firmly attached to the underlying tissue.
My guess is that the massage might have traumatized the delicate skin of your nostrils which might have stimulated either latent rosacea or telangiectasias to develop (broken capillaries). This would cause chronic redness. See your dermatologist for treatment, often lasers and/or medications will help.
Inflammatory reaction to Radiesse
Although uncommon, it is possible to have an inflammatory reaction to any dermal filler. If you have a history of inflammatory reactions be sure to notify your plastic surgeon or dermatologist before the injection. They may choose to inject a small amount of the filler into a inconspicuous area under your skin to determine how you'll react. For an injection on the nose, is best to visit with a board-certified plastic surgeon so that they may determine if you have an excess of Radiesse, if the Radiesse needs to be removed, or if you may be treated with an injection of another medication to help alleviate your inflammatory response.
The nose is an extremely complex structure with very sensitive skin. Any injections into the skin envelope must be planned carefully and limited.