I think you may have actually been medicating for the CBD side effect. I found when I started taking CBD that it helped a lot with anxiety but made me a little drowsy and helped my sleep somewhat. Over the next week or two the drowsiness mostly went away and my sleep was back to normal but it still helped with anxiety.

Unless your poor sleep is driven by anxiety, CBD is probably not the best choice. Some strain of Indica pot is probably what you are looking for.