Is it possible for shoulder fluid to get infected?

Shoulder infection. It is possible for any joint to become infected. Septic arthritis can occur from hematogenous (blood stream) or lymphatic spread or from penetrating injuries or injections.
Yes. It is possible but typically rare. However, if there is any concern for an infection (redness, warmth, fevers, chills, drainage, swelling), you should seek immediate medical evaluation.