YOU SAID:

i fell asleep in my sleep which i dreamt of while i was sleeping in my sleep.

INTO JAPANESE

眠っている間に夢見ていた眠りに落ちました。

BACK INTO ENGLISH

I fell asleep while I was sleeping.

INTO JAPANESE

私は寝ている間に眠りに落ちました。

BACK INTO ENGLISH

I fell asleep while I was sleeping.