I am not saying the prophets are God. What I am saying is that the prophets have a tendency to speak like God in the first person. Which can make it difficult to use the OT when discussing the premises of the Trinity. This was an argument used by Muslims.
The key to identifying the difference between the two lies in the appearance of the one making the statement. Prophets were ordinary men who were known members of the community. Their presence was not a one time or sudden event. Whereas with the Angel of the Lord appeared at the moment of the announcement, and most often only for a few minutes.
Since you mentioned the Book of Isaiah the Angel of the Lord only appears once in the book of Isaiah. That is in Chapter 37 verse 36, and that particular chapter is most indicative of the point I am making.
When King Hezekiah was about to acquiesce to the king of Assyria Isaiah sent a message to Hezekiah which you will notice begins with Thus saith the LORD God of Israel. While in verse 36 we find:
Isaiah 37:36 KJV Then the angel of the LORD went forth, and smote in the camp of the Assyrians a hundred and fourscore and five thousand: and when they arose early in the morning, behold, they were all dead corpses.
What we find in this verse is a quick and decisive action by the Angel of the Lord.
In all 63 instances of The Angel of the Lord appearing in the Old Testament you will find that the Angel appeared and only remained as long as necessary to accomplish the will of God.
Hope this helps.
The prophets were always sent, and the books declare each prophet's name and to whom they were sent. When we read the book of Isaiah we know that the prophet was Isaiah, and he was speaking on behalf of God, relaying God's words to the people.
Isa. 1:1, Isaiah sent to Judah and Jerusalem:
"The vision of Isaiah the son of Amoz, which he saw concerning Judah and Jerusalem..." (KJV)
Isa. 13:1, Isaiah speaking the prophesy to befall Babylon:
"The burden of Babylon, which Isaiah the son of Amoz did see." (KJV)
By studying through both the OT and the NT we can determine that the angel of the Lord in the OT was the prefigured Christ.
"20 Behold, I send an Angel before thee, to keep thee in the way, and to bring thee into the place which I have prepared.
21 Beware of him, and obey his voice, provoke him not; for he will not pardon your transgressions: for my name is in him.
22 But if thou shalt indeed obey his voice, and do all that I speak; then I will be an enemy unto thine enemies, and an adversary unto thine adversaries." (KJV)
The angel had the authority and name of God. He also was the warrior for the people.
In Exodus 3:2 the angel of the Lord appears to Moses in a flame of fire, in a burning bush, and verse 6 He identifies himself as
"...I am the God of thy father, the God of Abraham, the God of Isaac, and the God of Jacob. And Moses hid his face; for he was afraid to look upon God."
In contrast to other instances when angels forbade a man to worship them (Gabriel in Dan. c. 9 -12), this angel accepted Moses worship.
This is also the same "captain of the Lord's hosts" of Josh 5:14-15 whom Joshua worshiped. Just as the angel told Moses in Ex. 3:5, the captain of the host told Joshua to remove his shoes for the place he stood was holy. It is the same angel of the Lord whom David worshiped in 1 Chron. 21: 15-19.
In Judges 13:16-21 the angel of the Lord appeared to Manoah and his wife to tell them of their son Samson, and Manoah asks for the angel's name. The angel said in verse 18 that His name was secret.
Rev. 19:12, speaking of Christ, the warrior of His people (Psa. 34:7; Dan. 12:1),
" His eyes were as a flame of fire, and on his head were many crowns; and he had a name written, that no man knew, but he himself." (KJV)
In Judges 13:20 the angel of the Lord ascends in the flame of the altar, just as he had appeared to Moses in the flame of the burning bush. The flames, the fire are symbols of God, and especially of His judgment. (See Rev. 1:14; 2:18; Psa. 83:14; Isa. 10:17; Isa. 30:30, etc.)
Hosea 12:3-5 makes it clear that the angel Jacob had wrestled with in Gen. 32:24-25 was the "the Lord God of Hosts."
The word angel means "messenger". The angel of the Lord was the very special messenger of God better than all the angels (Heb. 1:4), the very special begotten Son of God (Heb. 1:5), the one who created all things (Col. 1:16) which would include the angels (Psa. 148: 1-6), the one sent to be the savior for all who will call on His name through the gospel of Christ (Rom. 1:6; 1 Cor. 1:2; 2 Tim. 1:9).
Benson's commentary on Exodus 3:2,
"Exodus 3:2. The Angel of the Lord appeared to him — Not a created angel, but the Angel of the covenant, Christ, who then and ever was God, and was to be man, and a messenger from God to man. He, termed the Angel of God’s presence, (Isaiah 63:9,) had wrestled with Jacob, (Genesis 32:24;) and had redeemed him from all evil, (Genesis 48:16;) and afterward conducted his posterity through the wilderness, 1 Corinthians 10:4. These his temporary appearances were presages of his more solemn mission and coming, on account of which he is fitly called the Angel or Messenger. That this angel was no creature, appears from his saying, I am the Lord, a language which angels never speak; but, I am sent from God — I am thy fellow-servant. In a flame of fire — Representing God’s majesty, purity, and power, and showing that he was about to bring terror and destruction to his enemies, and light and comfort to his people, and to display his glory before all. The bush burned and was not consumed — An emblem of the church now in bondage in Egypt, burning in the brick-kilns, yet not consumed; cast down, but not destroyed; for God was in the burning bush, was and always will be present with his people in their sufferings; Isaiah 43:2; Daniel 3:25." Source: here
Deuteronomy 18:22 "If the prophet speaks in the name of the Lord, and the thing does not occur and does not come about, that is the thing the Lord did not speak. The prophet has spoken it wantonly; you shall not be afraid of him."
If they speak of something that never happens they're not a prophet. With this it's not always completely clear because you have to look at the details. Like if the person gives a timeline for when they say it'll happen. Like before that generation dies out, or something that can be used as a proof it happened like they said in the time period they said, or it didn't. Something that can be verified.
What ever the person says would have to agree 100% with what god already established, because it's everlasting and unchangeable. (Deuteronomy 13, Ezekiel 37:26)
So if they speak any objection to what god taught they do not speak for God.
Miracles are not evidence that they speak for god. Deuteronomy Ch 13 describes how even false prophets can do miracles. God allows it because he says he's testing to see if you love him with all your heart and soul.