For whom are the pronouns "my" and "I" used in the first stanza of this poem?

The words "my" and "I" in the first stanza of the poem describe the chimney sweep. He is telling his own story, using the first person voice.
In the first two lines, the chimney sweep, speaking to those people who are comfortably well-off enough to read a poem, explains how he became a chimney sweep. He tells his audience that his mother died when he was very young, then that his father "sold" him to a man who would make money having very young boys climb down narrow chimneys to clean them. Of course, actual slavery was illegal in England at that time, so the man gave the father some money and took the boy off his hands.
This was one of the worst jobs in nineteenth century England. It relied on young boys being kept half-starved to be thin enough to fit down the chimneys. Rather than go to school, they did hard work all day. Many of them died young.
Presumably, the boy's parents were very poor. His mother would probably have protected him, but once she died, his father apparently felt he could not take care of the young child. The chimney sweep ends the stanza by saying that he sweeps chimneys and sleeps in soot. The "I" in that final line also refers to him.