Some commentaries have the timeline somewhat reversed, that Hezekiah was sick before Assyria came to Jerusalem. And that the prophet came to him while the armies were setting up camps. When Isiah came to Hezekiah, his prayer wasn't simply for himself. His concern was also for the nation. He asks God to remember all the good he's done, I think sometimes we all feel the same way, as if anyone deserves something from God. Hezekiah was able to do what he did, just as each of us can do what we do because God equips and allows us to do so. No-one knows the nature of the illness, it was a common practice to put a paste of figs on body sores, perhaps the malady manifested in such and the act was simply one of obedience. In any case God saved Hezekiah for His purposes. The miracle of the shadow retreating has a lot of differing opinions but most all agree that the earth and sun did not move backward. The miracle was also regional, no-where else was a retreating shadow noted. For God to make a shadow retreat, or appear to retreat, He simply needs to light up the last 10 steps. If God can produce a thick darkness in Egypt and light in Goshen then certainly He can light up 10 steps.