Only one side of my nose gets stuffy when I lie down. Will lying down the other side help?

Normal nasal cycle. Your nose is meant to filter the air you breathe. The normal nasal cycle describes an alternating congestion of each side of the nose every 90 minutes. The congestion comes from the dilation of blood vessels in the turbinates and septum. If you feel stuffy, there may be an additional blockage like a deviated septum, allergies, enlarged turbinates. Find a local ENT to evaluate your nose and airway.
Turbinates. This is most likely related to the turbinate tissue in your nose swelling. You may also have a deviated septum. Nasal steroid spray or surgery may be helpful.