Can a thyroglossal cyst be diagnosed if at the time the ultrasound is done, the swelling has completely gone down due to antibiotic treatment?

Perhaps. As long as the thyroglossal duct cyst is a few millimeters in size it should be visible even if not palpable. However, why do you think that you have a thyroglossal duct cyst? Was this demonstrated before on ct or ultrasound?