is tự necessary?
No. But it indicates the sense that "you do something yourself". Without it, the meaning remains unchanged.
Unchanged from what? From the English sentence? -:
Why does this one require both "tự" and "bản thân"? Most of the others in this lesson use just one or the other.
I think that "tự" is there just to stress the fact that the punishment is self-inflicted.
Oh no house elves, you should not punish yourself =)))