Isaiah 38:1-14 ~ In those days Hezekiah was sick and near death.

We are in this transitional section of Isaiah of chapters 36 through 39. This is the place where Isaiah transitions from Judgement to the Glory of the coming messiah. The first part of this section, chapters 36 & 37 involved King Hezekiah's trust in God and deliverance when Sennacherib's Assyrian army besieged Jerusalem.
The second part is chapters 38 & 39 we will see Hezekiah's failure to trust God and his consequent judgment by God when the Babylonian envoys peacefully visited Jerusalem.
In chapters 36 & 37 we saw Judah's deliverance accomplished, and in chapters 38 & 39 we hear Judah's captivity announced.
This is where emphasis on Assyria ends and emphasis on Babylonia begins.
The events in these chapters 38 and 39 predate those of chapters 36 and 37 by a few months. Isaiah placed them here, out of chronological order, to make them a historical prologue to chapters 40 through 66, which focus on the Exile and the return to Jerusalem.
This section opens with Hezekiah contemplating death (38:1a) and ends with him contemplating life (39:8). In between, Isaiah delivered two messages to the king (38:1b-7; 39:3-7). Hezekiah's dedication (38:8-22) followed the prophet's first message, and his defection (39:1-2), precipitated the second message.