I do not see any possibility of getting a doctor to inject something they have not prescribed, does not have guaranteed sterility, does not have solid science behind it and is not registered for therapeutic use in Australia. If something went wrong they would not have a leg to stand on in court trying to defend against malpractice. It might be bad enough to qualify as criminal negligence or cause them to lose their medical license. The uncertain sterility issue alone is an extremely good reason to never inject anything peptide like anywhere except under the skin, unless it came from a proper pharmacy company with standards and inspections etc. If you get a small infection just under the skin from a few bugs, it is very unlikely to kill you, the same near the spine is an incredibly serious infection, that could kill, cause permanent damage or at least require weeks of intravenous antibiotics in hospital.
I personally do not think those peptides ( TB500/BP157 ) have good evidence that they work, are minimally if at all tested in humans, despite everyone online saying how great they are. If you want to use them - orally or subcutaneously , if s/c somewhere sensible like the stomach, nowhere near any joints. HGH probably does improve healing but also has side effects. Doctors do not use it for faster healing as the risk to benefit ratio is not thought to be worthwhile.