Fighting against English vowels

I think Japanese is one of the most difficult languages, but its pronunciation isn't so difficult, I think.

There are only five vowels in Japanese. But English has 22 vowels! 22!!
It's very difficult for Japanese to distinguish and pronounce English vowels.

For example, followings are same pronunciation for Japanese.
luck - lack
stamp - stump
bird - bard

I'm training English pronunciation using the text book "Eigo mimi" (= English ear)
It shows tongue position etc... by pictures.

I'm training every day but it seems that there are many pronunciation using the back of the throat in English unlike Japanese so my throat hurts, sometimes I feel like throwing up. Is it right training?