It sounds like your infected cyst on the neck has not improved with the current medications, so seeing a specialist is a good next step. You should consult a dermatologist or a general surgeon for this issue. A dermatologist can manage skin infections and related conditions, while a general surgeon can assess whether the cyst needs to be drained or surgically removed. If the infection continues despite the prescribed antibiotics and anti-inflammatory drugs, a specialist can provide further evaluation and recommend additional treatments. Please seek prompt medical attention to avoid complications.