I strongly suggest you go to a pulmonologist and arrange for a sleep study. Snoring usually indicates sleep apnea, which means you stop breathing intermittently throughout your sleep cycle. Some people need a CPAP machine, but since I travel so much, and my apnea is very strange and uneven, I was prescribed an apnea mouth guard, which was made by my dentist. Insurance often covers it, and I take it with me everywyere. I was only a light/intermittent snorer, but I always felt exhausted in the morning after a 'good night's sleep". The mouth device (like one you use for grinding your teeth, but upper and lower for the apnea device) is small, unobtrusive, and weighs almost nothing, which is important on the Camino!
By the way, my partner, a LOUD snorer who now does have a CPAP, though he too has an apnea mouth guard for travel, tried those nose strips for years, and they never worked at all for him . . . Good luck.