In an intramuscular injection this is always tested by the nurse and this complication is far rarer than a nerve injury by the syringe. But in billions of cases anything can happen.
Yes, they mandated a test to check if it was being injected into a vein.
Pretty common test as well, pull the plunger back on the syringe if blood comes up you hit a vein.
A lot of drugs have this test, particularly drugs that should be injected in fat or muscle.