I am the man that hath seen affliction - Either the prophet speaks here of himself, or he is personating his miserable countrymen. This and other passages in this poem have been applied to Jesus Christ's passion; but, in my opinion, without any foundation.

the man

Lamentations 1:12-14 Is it nothing to you, all you that pass by? behold, and see if there be any sorrow like to my sorrow, which is done to me...

Job 19:21 Have pity on me, have pity on me, O you my friends; for the hand of God has touched me.

Psalm 71:20 You, which have showed me great and sore troubles, shall quicken me again, and shall bring me up again from the depths of the earth.

Psalm 88:7,15,16 Your wrath lies hard on me, and you have afflicted me with all your waves. Selah...

Isaiah 53:3 He is despised and rejected of men; a man of sorrows, and acquainted with grief: and we hid as it were our faces from him...

Jeremiah 15:17,18 I sat not in the assembly of the mockers, nor rejoiced; I sat alone because of your hand: for you have filled me with indignation...

Jeremiah 20:14-18 Cursed be the day wherein I was born: let not the day wherein my mother bore me be blessed...

Jeremiah 38:6 Then took they Jeremiah, and cast him into the dungeon of Malchiah the son of Hammelech, that was in the court of the prison...

his wrath. That is the wrath of God

"And we all do Fade as a Leaf, and Our Iniquities, Like the Wind, have Taken us Away. "
Isaiah lxiv. 6.--"And we all do fade as a leaf, and our iniquities, like the wind, have taken us away." Here they join the punishment with the deserving cause, their uncleanness and their iniquities, and so take it upon them, and subscribe to the righteousness of God's dealing. We would say this much in general--First, Nobody needeth to quarrel God for his dealing. He will always be justified when he is judged. If the Lord deal more sharply with you than with others, you may judge there is a difference …
Hugh Binning—The Works of the Rev. Hugh Binning

The Ambassadors from Babylon
In the midst of his prosperous reign King Hezekiah was suddenly stricken with a fatal malady. "Sick unto death," his case was beyond the power of man to help. And the last vestige of hope seemed removed when the prophet Isaiah appeared before him with the message, "Thus saith the Lord, Set thine house in order: for thou shalt die, and not live." Isaiah 38:1. The outlook seemed utterly dark; yet the king could still pray to the One who had hitherto been his "refuge and strength, a very present help …
Ellen Gould White—The Story of Prophets and Kings

Meditations for one that is Like to Die.
If thy sickness be like to increase unto death, then meditate on three things:--First, How graciously God dealeth with thee. Secondly, From what evils death will free thee. Thirdly, What good death will bring unto thee. The first sort of Meditations are, to consider God's favourable dealing with thee. 1. Meditate that God uses this chastisement of thy body but as a medicine to cure thy soul, by drawing thee, who art sick in sin, to come by repentance unto Christ, thy physician, to have thy soul healed …
Lewis Bayly—The Practice of Piety