Very good answer, Paigey!

Your doctor would be the best to answer your question about being tired, but I think it has something to do with you not having NREM. last two stages of NREM, stage 3 and 4 is when you sleep the deepest sleep and when body restores, repairs and re-energizes itself. So you are probably without these benefits of deep sleep and that may make you tired. Also, waking up that many times a night and having hard time falling asleep can make you feel not rested as well.

People do ask this question here from time to time if lucid dreams make you tired. Most of the answers is no. To the contrary, they make us happy and energized. But the story may be different, if all your dreams are lucid and especially if you lack NREM sleep. Sorry about that. Hopefully your doctor will be able to help to get you more restfull sleep. Good luck.