Can Radiesse be removed from my lips?

This is awful! Poor you. There is no reason that talking should affect the injectible. Who IS this doctor. It sounds like he should be reported. From the info below, it sounds like our doctor didn't inject it deeply enough since you have nodules. It also says that it shouldn't be used in the lips.
Radiesse in any location will generally last about a year. Removal is quite difficult and would involve making some kind of incision to remove the underlying material.

I found this info:
Radiesse is a skin filler which can last longer than hyaluronic acid fillers (e.g., Restylane and Juvederm). It can improve lines and increase volume in certain areas for approximately 12-18 months. Radiesse is injected at a deeper level than collagen and hyaluronic acid products. In fact, if it is not injected deeply enough, nodules or lumps can form.
After Radiesse has been injected, there have been reports of nodule formation in some patients. This is most commonly seen for Radiesse injections in the lips. A very important point is that Radiesse should not be used in this area.
Can you remove Radiesse once it’s been injected? Answer: Only Sometimes.
Radiesse is a combination of a water based gel and calcium hydroxylapatite. The water based gel fills skin for up to 3-4 months. After that, the collagen that forms around the calcium compound causes long term filling.
It’s unlikely that puncturing a treatment area with a needle and squeezing will result in a lot of gel being squeezed out. This is especially the case for Radiesse that was injected at a proper depth. “Poking” an area that has misplaced Radiesse just under the skin may work for a few days after treatment.
After 2 or more weeks, if there’s a “lump” just under the skin, a small incision can be made, usually with a small scalpel after injecting a numbing medicine, and the Radiesse “lump” can be removed.
Removal of deeper Radiesse injections is a more involved procedure, and this may change the texture of the area afterwards.
Although complications can happen to anyone, you don’t want to deal with them if possible. The most important point here is that a medical doctor who has experience in Radiesse injections will give you your best chance of success. He or she will know how deep to place the injections, how much to use, and where not to inject.

And this was writted by an MD;

Radiesse is a dermal filler that is 30% powdered calcium hydroxylapatite (CaHA) and 70% gel carrier. After the Radiesse is injected, the material remains gelatinous for a few days. During this time, it is possible to use a needle to make a small puncture wound through the skin and into the Radiesse, which would allow some of the mateial to be squeezed out through the puncture wound.
Shortly after the Radiesse is injected, collagen starts to form around the microscopic calcium hydroxylapatite (CaHA) particles. After about 2 weeks, enough collagen has formed to make the Radiesse adhere to the surrounding tissue. At that point, the Radiesse may no longer be squeezed out like jelly through a puncture wound.
If the Radiesse is very superficial, it still may be removed under local anesthesia by deroofing the skin over the Radiesse and teasing out the nodule with a sharp needle.
If it is necessary to remove the Radiesse after 2 weeks, it may be necessary to have it surgically removed, which may leave a defect in the skin. Keep in mind, that even though the calcium hydroxylapatite (CaHA) particles will last for 12-18 months, the gel carrier will only last 3-6 months. That means that about 2/3 of the Radiesse will dissolve without treatment within 3-6 months.
Using a laser or an IPL on the treated area may hasten the breakdown of the gel carrier.
Unlike Hyaluronic Acid fillers such as Juvederm, Restylane and Perlane, there is no chemical available to safely dissolve the calcium hydroxylapatite (CaHA) particles.

Good luck. I suggest that if your dermatilogist doesn't want to help you that you report him and find someone else.