Who is injecting Botox and Juvederm
I am not a lawyer and every state has its own laws governing this. What I can tell you the definition of "training" does not confer expertise on any injector, nurse practitioner or physician. There are folks who are "trained" that spend an hour with a nonphysician sales rep who shows them how to inject Botox or Juvederm in a crash course. The company obviously wants to put their products in the hands of as many injectors as possible. Then you have physicians like dermatologists and plastic surgeons who "train" for several years and learn the anatomy, the nerves, the arteries, the veins, the muscles of the face in detail and are supervised by board certified physicians that teach them how to inject and they perfect their skills over years.
The two are not equivalent.
The answer varies state by state, but to give you some reference, in Wisconsin NP's still need supervision. That level, unfortunately, is way too loose. The supervising physician can be of almost any discipline (core disciplines vs family practice, er, anesthesiology, psychiatry), and practice only within around 100 miles of the injector. That's obviously an accident waiting to happen. One other consideration is that many of the vendors will not dispense to someone who is not a physician. So you won't be able to even order your botox or fillers.
Would you rather have a doctor or nurse inject your face?
In Virginia, nurses who have been trained are allowed to inject Botox and fillers. I think you should ask yourself who you would want to inject you? Plastic Surgeons undergo years of training in order to be able to practice medicine and surgery. This includes at least five years after medical school. Nurses are able to fully practice after one year of nursing school; the nurses injecting usually did go to a weekend course, but is that really what you want?
Nurses injecting Toxins and Fillers
In some states these providers can do many things, including cosmetic injections. The bigger question is whether you want someone that understands the anatomy of your vessels, nerves , muscles, etc. to be injecting you or someone who saw one and will do one. Also, who will care for you in case of problem or bad result. think about that before choosing.
Laws for what nurse practitioners can and can't do vary state-to-state. There are some new laws coming down in NV specifically that were intended to deal with nurses performing certain duties for patients who are dying and in critical care mostly in rural areas; however, since much of the writing is lose, some NPs are using this to mean they no longer need MDs over them in any capacity. So... what's intended and what happens in practice is variable. Until someone gets harmed, and then the rules will be tightened again. Which is very sad.
In Texas the nurse has to be supervised by a physician and he has to be immediately available. In most states rules are similar. You should go to a surgeon board certified by the American Board of Plastic Surgery. Any nurse involved in these practices should be safe.
Can Nurse Practitioners work without a physician and do cosmetic treatments?
This really is a state law question. Check with the nursing board for your state. They should be able to give you the answer. Many states are loosening their restrictions on nurse practitioners to fill a perceived void in care or possibly to decrease governmental costs, however I don't know of any state as of yet that allows them to practice any medicine without a collaborating physician.