When you approach the doors of the Chomper's Dental office on the lower floor of the Medical Pavilion, you will see the corpse of a Splicer hanging through a broken window. Look straight forward through the window, & you will see a key hanging on the wall beyond. Use the Telekinesis Plasmid to bring the key to yourself, & press interact button to acquire it.
Go to the door of Chomper's Dental & look for a smashed glass pane next to the locked door to Chomper's Dental; if you've done it right then there should be a machine gun turret on your left that is situated behind the window (be careful if you haven't destroyed the turret yet), & the doorbell to access the room should be on your right. Use the Telekinesis Plasmid & aim into the room. You should grab a golden key that will grant you access; use the interact button to pick up the key.
An important note: Do not let go of the key or you will be unable to get access into the room after you throw away the key.