I had a sudden onset of shoulder pain that sent me to the doctor's office in a hurry. I couldn't remember any kind of injury or recent illness. The bill I received describes the treatment as a "diagnostic injection." What does that mean exactly?

You may have had a steroid injection into the shoulder or one of the nearby joints. This is an anti-inflammatory drug given locally right to the potential source of the problem.
It's called diagnostic because the doctor is using it to figure out what's wrong. This step can cure the problem for some patients and avoid expensive imaging studies such as MRIs.

If you got good pain relief from the injection, then it's likely there was some swelling or inflammation in the joint pressing on soft tissues or a nerve causing the pain. If the pain relief was only temporary (an hour, several hours, a day up to a week), then more tests may be needed.