You tell Mr. Hissy pants that he NEEDED to go to that doctor and that trip will make him better soon! There's no need to get all in a huff with you over trying to help him get better!

That reminds me of My RB Sambo who use to get mad at me and ignore me no matter what I tried... What I learned from that is two can play that game and he didn't like it when I responded to his ignoring me by ignoring HIM! Try THAT on His Hissy pants and see what happens!