Different states have different regulations about whether nurse practitioners or physicians are allowed to do injection procedures. You should consult your state medical society about this and consider the experience of the condition as well as their accessibility to medical care in the event of a complication.
Yes. A nurse can legally inject fillers. However, injectables, whether they be fillers or Botox, require medical expertise as well as a keen artistic eye. Plastic surgeons have the training, skill and expertise to deliver both. Best of luck.