Prime Care Medical Center in Selmer, Tennessee - Family . Health (Just Now) The current location address for Prime Care Medical Center is 270 E Court Ave, Suite B, Selmer, Tennessee and the contact number is 731-645-7932 and fax number is 731-645-5195.The mailing address for Prime Care Medical Center is 1804 Highway 45 Byp, Suite 604, Jackson, Tennessee - 38305-4436 (mailing address contact ....