What else can I do against the pain except for a cortisone shot and arch support for my supination?

Other than cortisone and arch support, you can certainly opt for orthotics, which can be beneficial in supination. However, don't just buy any random orthotics. Visit a good podiatrist, and then get custom-built orthotics for supination. They would refer you to wear orthotics after closely observing your feet condition. You are likely to get relief from the pain within a few weeks.