How do you get swelling to go down in new tragus piercing?

There should be no swelling if the piercing was done by a professional body piercer in a licensed and inspected facility. Swelling is generally caused by over using a cleaning solution or the piercing was done by a piercing gun (which when it comes to Tragus piercings is not only dangerous it's also a violation of most standing health guidelines for body piercing). So the best bet is to irrigate the area with warm running water in the shower while moving the jewellery, if the swelling is to the point where the jewellery can't be moved then you need to see a professional body piercer to have the jewellery changed to something that will allow the piercing to discharge and thus relieve the swelling.