Medical ID comes up when I press phone icon, can't be canceled

You can read about this problem on the Apple Support website. It may be some kind of software bug. Or check for updates iOS to the latest version, as well as the program with your Medical ID. When I installed practice management software on my mac, I had no problems, although maybe because it is a program on a PC. Anyway, it helps me manage all my deeds. Try to create a copy of your data in iCloud and reset your phone. I always do this when I have problems with some application. I hope that my advice was helpful to you.