The first thing we need to understand is that the Hebrew word מַלְאָךְ (mal'akh) literally means "messenger." It can refer to human messengers (Hag. 1:13) as well as spiritual messengers (Gen. 22:11; the latter is what we commonly refer to as "angels"). A related noun מַלְאָכוּת (mal'akhut) derived from the same triliteral root מל"ך means "message" (Hag. 1:13). The English word "angel" comes from a loose transliteration of the Greek word ἀγγελός (angelos). But, like the Hebrew word מַלְאָךְ, it also means "messenger" and can refer to human (Jam. 2:25) and spiritual messengers (Matt. 1:20).
All that being said, now we can interpret Gen. 48:15-16.
טו וַיְבָרֶךְ אֶת יוֹסֵף וַיֹּאמַר הָאֱלֹהִים אֲשֶׁר הִתְהַלְּכוּ אֲבֹתַי לְפָנָיו אַבְרָהָם וְיִצְחָק הָאֱלֹהִים הָרֹעֶה אֹתִי מֵעוֹדִי עַד הַיּוֹם הַזֶּה טז הַמַּלְאָךְ הַגֹּאֵל אֹתִי מִכָּל רָע יְבָרֵךְ אֶת הַנְּעָרִים וְיִקָּרֵא בָהֶם שְׁמִי וְשֵׁם אֲבֹתַי אַבְרָהָם וְיִצְחָק וְיִדְגּוּ לָרֹב בְּקֶרֶב הָאָרֶץ
15 And he blessed Yosef, and said, "The God, before whom my fathers Avraham and Yitzchak walked, the God who shepherds me ever since until today, 16 the messenger who redeems me from all evil, bless the children, and let my name be named on them, and the name of my fathers, Avraham and Yitzchak, and let them grow into a multitude in the midst of the earth.
We must focus on the idea of redemption from evil. This is not a function of any mere human messenger. In the Tanakh, humans redeem property (Lev. 25:25), houses (Lev. 27:15), fields (Lev. 27:19), relatives via Levirate marriage (Ruth 3:9), etc. However, it is Yahveh who redeems His peoples' soul (Psa. 69:18) and life (Psa. 103:4; Lam. 3:58); Yahveh redeems His people from the power of the grave (Hos. 13:14) and from death (Hos. 13:14). Numerous times, Yahveh is referred to as "the redeemer" (הַגֹּאֵל) (Isa. 47:4) of His people.
Keli and Delitzsch wrote,
This triple reference to God, in which the Angel who is placed on an equality with Ha-Elohim cannot possibly be a created angel, but must be the "Angel of God," i.e., God manifested in the form of the Angel of Jehovah, or the "Angel of His face" (Isaiah 43:9)...
So, is the מַלְאַךְ יַהְוֶה (mal'akh Yahveh), God Himself?
In Gen. 28:18-22, Ya'akov anoints a stone and makes a vow to God, saying, "If God will be with me, and will keep me in this way that I go, and will give me bread to eat, and raiment to put on, so that I come again to my father's house in peace, then Yahveh shall be my God."
Notice that Ya'akov makes a vow to Yahveh, i.e. God.
A few chapters later, in Gen. 31:11-13, Ya'akov states,
And the angel of God spoke to me in a dream, saying, "Ya'akov!" And I said, "Here I am!" And he said, "Now lift up your eyes, and see, all the rams which leap upon the cattle are ringstraked, speckled, and grisled, for I have seen all that Laban does to you. I am the God of Beit-El ("the House of God"), where you anointed the pillar, and where you vowed a vow to me. Now arise! Get out of this land, and return to the land of your kindred!"
Notice how "the angel of God" (lit. "messenger of God") identifies himself as "the God of Beit-El" and then says that Ya'akov "vowed a vow to me." When we go back to Gen. 28:18-22, you'll see that Ya'akov vowed a vow to Yahveh, God.
Therefore, the messenger who redeems Ya'akov from evil could be none other than Yahveh Himself, especially because such a function (i.e., redemption from evil) is something that only Yahveh can do, being "the redeemer of Israel" (Isa. 49:7).