A 35-year-old woman presents to an urgent care clinic complaining of significant throbbing pain in her left middle finger after accidentally dropping a heavy cast-iron pan on it approximately three hours ago. She reports no prior injury to the finger. On examination, there is noticeable swelling and a dark purplish discoloration beneath the nail plate, involving roughly 70% of the nail bed. There are no obvious external lacerations or avulsions of the fingertip, and capillary refill is brisk. She rates her pain as an 8/10. X-rays of the finger reveal no evidence of a fracture or dislocation. Complete blood count shows a WBC of 8.5 x 10^9/L, Hemoglobin of 13.8 g/dL, and Platelets of 280 x 10^9/L. What is the most probable diagnosis for this patient's condition, and what is the immediate, least invasive management strategy to alleviate her symptoms?