Reza: This is quite an interesting one. You're right about the first bit, "I am an English teacher" does or should change meaning depending which word is stressed more. But, people often don't pick up on that, and need a more detailed sentence to confirm it.
Thats when you would use either of your two sentences below to clarify the meaning.

1)I'm a teacher who teaches English.
2)I'm a teacher from England.


The same can be applied - to a point - to the second sentence.

I'm an English history teacher. means you teach history (I would guess world history) but that you are English.

However, if you wanted to explain that you are a teacher that teaches English history I think the emphasis would be on two words; "I'm an English history teacher.