Full answer with lots of help:
They took from me something near to my heart. I crossed the Atlantic, my short became long, but I was still essentially myself.
Start with "whinged", remove 'g' near the middle of the word to give "whined". Crossing the Atlantic here refers to the two words being British vs American use. The short sound of 'i' in the word is now a long sound but they mean the same thing. (this entire part is @M Oehm's credit, not mine.)
I gave up heroin. I introduced my companions to my friend Syrah.
Removing 'h' (slang for heroin, thanks to @Deuvosi) from "whined" gives "wined" which means entertaining people with wine (thanks @stackreader for Syrah = wine).
Once accustomed to a life of comfort, I left all ease behind. I had no place to rest, but I was always of two minds—to meander in and around the trees, or to blow through and past them?
Leaving all ease behind = remove 'e' from "wined", giving "wind" which could mean both meandering and blowing.
I chased a husbandman's wife until she attacked me in her usual manner. I left, diminished, but I felt no loss.
Husbandman's wives cut off tails ala 3 blind mice, so taking away 'd' gives "win" (no loss there).
I made a teacher mad, and she tore my head off. This made me one of the popular kids.
Taking off the 'w' gives "in" - being one of the "in crowd" means you're cool (or so they say).
And now I am here before you, nearly unrecognizable—but a fraction of what I once was—but focus your sight just on my head. You'll see I was here all along.
Looking at just the start of "in" gives you - surprise, surprise, "I" which was indeed here all along!
The starting point, "whinged", means to complain, which is certainly reflective of the tone used by narrator! Well played, OP.