How can we identify, sometimes, the angel of the Lord as God if the prophets also spoke as God? 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.