‘And the angel of Yahweh found her by a spring of water in the desert regions, by the spring on the way to Shur.'
There is no suggestion that she is in difficulties, (unlike the next time when she tries the same move under totally different circumstances (Genesis 21:15-16)). As a young, healthy and determined woman she has made her way fairly easily and is almost on the borders of Egypt and safety. (For Shur as close to Egypt see Genesis 25:18; Exodus 15:22; 1 Samuel 27:8). But Yahweh has seen her flight and is cognisant of the fact that she carries Abram's son. Thus He will not allow her to flee into anonymity in Egypt, and He therefore seeks to restore her to Abram.
“The angel of Yahweh found her”. He had been sent on a specific mission and ‘finds' her where he knows she is. The angel of Yahweh is a somewhat mysterious figure. In some ways he is distinguished from Yahweh, yet in others he is identified with Him. He is as it were an extension of Yahweh when a personal physical presence is required, just as the Spirit of God is seen as an extension of Yahweh when some remarkable invisible activity occurs. He is preparatory to the revelation of Jesus Christ as God's mediator with men.