Sterilization Before Injection?

Hi, I had my shoulder joint injected w/cortisone yesterday. Before the injection, the nurse sterilized the top of my shoulder area w/alcohol. However, the doctor injected the steroid into a different area (my back, which he said was the joint) & that area had not been sterilized. I am now in a panic. I already know that there is a slight risk of infection when an injection is given in a joint. Does the fact that the area was not properly steralized increase the risk of infection? Should I scared?

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