u/Matagorda, u/Nylund -- if the obstructed nostril is due to a deviated septum, my sleep doctor suggested I try a nasal dilator at night as an alternative to surgery. I bought something similar to this https://www.amazon.com/dp/B07NMTQM8M with different sizes so I could find my right size. They work great. Now I can sleep on both sides and breathe easy.
I went through a sleep study. I tried a CPAP for a month. I couldn't wear the full-face mask, and the alternative (a nose pad) meant I had to tape my mouth shut every night to keep the air in. I gave it a month and concluded that CPAP wasn't solving anything. I wasn't sleeping any better, and I sleep on my side anyway, which made the CPAP uncomfortable. Now I'm trying a prescription mouth guard, which is also uncomfortable. The quality and quantity of my sleep don't seem to be affected by any of these cures.
u/HMJ87 - I also have a deviated septum, which prevented me from breathing through my nose when I lay on on my right side. My sleep doctor suggested I try some conical nasal dilators. That has been the best solution so far. They don't fix the snoring (although they are advertised that way) but they center my septum so I can breathe while lying on either side. I sleep better with those. Start with a multiple-size pack like this https://www.amazon.com/dp/B07NMTQM8M so you can figure out the size that works best. They last for years.