Do doctors or nurses have to go on a botox/dermal fillers training course?

Not necessarily: It is not required but is a good idea. Consult a doctor with experience doing the procedure you are interested in. Ask friends who have had the procedure who they go to. A board certified plastic surgeon or dermatologist are a good place to start.

It Depends: Whether a doctor or nurse must have formal training in cosmetic injectables depends on the laws of the state in which they practice. In my state, for example, there is no law which requires that a doctor has taken a training course and there is some argument as to whether a nurse can legally inject. Therefore, the patient must be careful to choose a qualified injector!

No: Companies are legally obligated to sell their products to any licensed physician regardless of specialty or level of training. Some provide on-site instruction but it is mainly up to the physician to develop expertise through education pathways such as residency, fellowship, observation and instructional courses. Nurses can inject under the supervision of a licensed doctor. Know your injector!

Not necessary, helps: This is not always necessary but going on such courses may help to improve ones techniques by learning frp others experiences, approaches, devices, pain prevention, aftercare, etc.

For some it's part: For some specialties like dermatology, otolaryngology head and neck surgery and plastic surgery, expertise in Botox and dermal filler administration is part of residency training. Additional courses are taken to increase expertise and refine techniques. For pas, arnps and rns, responsible folks, will go to training courses to gain knowledge about these procedures they want to perform.