You are almost certainly dreaming, you just forget. As far as I know, people generally forget a lot of their dreams. You seem to be one of those who always forgets.
Everyone dreams in the paradoxical stage of sleep. You forget well.
You can experiment with multiple abrupt awakenings during the night. Not on an alarm clock, but for the other to wake up resolutely and at once. It is desirable in the paradoxical phase of sleep purposefully: sometimes it can be understood by some anxiety of the sleeping person. But, most likely, at random. - And immediately write it down if there are fresh traces of memories of a dream: they quickly fade from memory upon waking and normal.