Sorry to hear that when you sleep on one side your nostril tends to get stuffed up, and that this is bothering you. I will give you my thoughts as to what might be going on, and ultimately I am going to recommend that you get evaluated by an otolaryngologist
aka ENT (Ear Nose Throat physician). There are radiator like structures in everyone’s nose called turbinates (inferior turbinate, middle turbinate, and superior turbinate) that have erectile tissue on them causing them to swell. These structures function to warm and humidify the air that passes through your nose before it makes it into your lungs. It is normal for one side of your nose to swell, while the other side shrinks down. This is called the nasal cycle, and it changes about every three hours. It is not uncommon for the dependent side (the side down) to have a bit more swelling when lying down. In most people their nasal passages are large enough that this doesn't make a largely noticeable difference. It is possible that your nose is narrow, and you are more sensitive to this change. If you always notice it is worse on one side verses the other, it is also possible that you have a deviated septum (the divider going down the middle of your nose is crooked). An ENT will be able to tell you if this is the case when they examine you.