Isaiah 37:14-38 is arranged in a simple chiasm:

A. Hezekiah prays in the temple, vv 14-20

B. Isaiah prophesies concerning Sennacherib, vv 21-29

C. Isaiah gives a sign concerning Judah, vv 30-32

B’. Isaiah prophesies concerning Sennacherib, vv 33-35

A’. Sennacherib killed in the temple of Nisroch, vv 36-38

The B section is itself a chiasm:

A. Taunt song of Daughter Zion, vv 21-23

B. Sennacherib’s boasts concerning Lebanon and the rivers of Egypt, vv 24-25

C. Yahweh’s plan, v 26

B’. Cities wither like grass and Sennacherib’s boast, vv 27-28

A’. Sennacherib removed, v 29

Back to the main chiasm: The two A sections are clearly parallel. As my colleague Toby Sumpter pithily put it, both are scenes of kings in temples, though the outcome for the two kings is opposite: Hezekiah’s prayer in Yahweh’s house leads to deliverance from the siege, a new Passover; Sennacherib’s worship of Nisroch ends in his death. The Be sections both contain prophecies about Sennacherib, emphasizing that he will not succeed in taking Jerusalem and that he is only Yahweh”s tool. The central section is Isaiah’s sign: Judah’s food supply will be restored, she will enjoy a Sabbath-year abundance, Judah herself will be a well-rooted, fruitful plant. The passage is about the preservation of Yahweh’s vineyard from the trampling beast, Assyria (cf. Isaiah 5).