Gothenburg Clinic Hours: Monday - Friday, 7:00 am - 5:00 pm. Saturday, 8:30 - 11:30 am. The Emergency Room is always open 24/7. In addition to in-person clinic visits, Gothenburg Health is excited to offer virtual clinic visits through our new Telemedicine offering, please call 308-537-4066 to schedule a virtual visit. 2021..