I feel angry when my sister takes my something

(Grammar Questions I Couldn't Answer)

I was doing questions about "When do you Feel Angry" (from my feelings slideshow in my Circle Time activity folder).

One of the students said, "I feel angry when my sister takes my something."

I corrected it--"something of mine."

"But why not 'my something' ?" the students wanted to know.

And this I couldn't answer. Is there some sort of rule about how possessive determiners can't be used with something ?

When I was talking about this with my Vietnamese wife, she asked me about the phrase, "my everything". 

"People say that right?" she asked me.  "Like, 'You are my everything' ?"

I agreed that this was a phrase in common usage.  But I couldn't decide if it was grammatically correct, or if it was a playful use of language that had become idiomatic.