In the canton of Valais there is the Valais Hospital Centre. This includes the two hospitals in the Upper Valais. The emergency ward is currently located in the Visp hospital. There is also a general practitioner's emergency practice in the Upper Valais:
Link to Visp Hospital
There is also a hospital in Brig. The new Oberwallis hospital centre will be built here in the next few years:
Link to Brig Hospital