I don't think is a good idea to take any kind of meds to fall asleep.
Like every meds you can become a dependent of it, if not physically, but mentally for sure. You'll start to relay on taking it just to fall asleep (going to bed will be association for taking med and this will result in a mental game)
If you stop the Nyquil, you will start sleeping better in a few days. It will take your body some time to get used to not having it, but you will eventually sleep better.
At your age is normal not to feel sleepy till late night hours, so, go to sleep when you are sleepy.
Stop worrying about falling asleep (you're getting the warm sensations in your limbs because you're getting anxious about falling asleep)
Try to avoid sleeping in front of TV and make your bedroom primarily a place for sleeping.
Incorporate bedtime rituals like listening to soft music, having a cup of herbal tea and relax for a while before going to bed(meditation, relaxation, warm bath)
Don’t eat a large, heavy meal before bed.