If you read Genesis 48:15-16 through, in context, it becomes quite clear that this "Angel which redeemed me from all evil" is just one poetic description of God. God, or the Angel of the Lord, redeemed—saved or rescued—Jacob throughout his life, from the fury of Esau (twice), from the machinations of Laban, from the threat of revenge by the Canaanites in response to the slaughter of Shechem, and finally from the famine and enslavement by the Egyptians.
That is the short answer. But what is meant by "the Angel" in the phrase "the Angel of the Lord"? Answering that will shed light on what is going on here. There are many instances in the OT in which a being called "the Angel of the Lord" speaks, and sometimes appears, to various people.
The description suggests a messenger of the Lord. The word for “angel” here, מֲלְאָךְ or malak, could be glossed “a messenger,” and while all the literal and standard translations use the phrase “the angel of the Lord,” the definite article is not actually appended to malak. So it is at 48:16: הַמַּלְאָךְ֩ means "the angel." So, you might wonder, why not use indefinite article, a (not the) messenger? Couldn’t this have been an ordinary angel? The context of the present verse makes it clear that this is another description of God himself.
That explains why theologians appear united in maintaining that various other instances of this word, followed by "of the Lord" (malak Yahweh) is best rendered “the angel of the Lord.” See, just for example, Gen 16:7, when the angel of the Lord speaks to Hagar. Because the phrases malak Yahweh and (the closely related) malak Elohim (“angel of God”) are often described as God or the Lord himself. This angel of the Lord consistently offers help, commands, advice, visions of the future, etc., in ways that indicate this is indeed God at work.
In the case of Gen 16:7, although the said angel does not do anything other than to speak to Hagar, what he says is, “I will multiply thy seed exceedingly.” (16:10) That is a thing only the Lord could do. Later, the text says “she called the name of the Lord”—no mere angel—“who spake unto her, Thou God seest me.” (16:13)
In a later chapter, we will again find that “the angel of God called to Hagar out of heaven” (Gen 21:17); this suggests that this is a disembodied voice representing the word of God himself. But the angel of the Lord does not only speak. The phrase is used, in Exodus, to refer to the pillar of fire and of smoke leading and following the fleeing Israelites (Ex 14:19); and to Manoah, the mother of Samson, the “angel of God” appears in the form of a man (Judg 13:9).
One of the more telling passages is when “the angel of the Lord appeared unto [Moses] in a flame of fire out of the midst of a bush” (Ex 3:2), and two verses later, we have “God called unto him out of the midst of the bush” (Ex 3:4). This indicates that this is God himself, or an earthly appearance (a theophany, and in particular, a shekhinah, again) of God. Many commentators have inferred that such theophanies, if not strictly identifiable with God himself, could be an appearance of the pre-incarnate Christ, especially insofar as the angel of the Lord is sometimes spoken of as being distinct from the Lord (or, as Christians say, from God the Father). But to really sort out this question would require that we get quite deep into theology.
