No expert, but I'm pretty sure I suffer from mild sleep apnea myself and my dr. told me it's very common. Was it like half or the third of the population here suffers from some level of sleep apnea, by his words. I'm not fat or heavy either. For me it's periodical and I think stress might be one thing to trigger it. I did do a sleep study test with monitors on for one night by dr.'s presricption, but that night I didn't show sings of sleep apnea, so I didn't get the CPAP machine.
Anyway the way you described what your gf told you, to me it sounds like having some level of sleep apnea. And yes nostral/sinus tightness is one thing to induce sleep apnea. Nasal spray before bed, breathing strips and even surgery in some cases are all used treatment, if the nasal pathway is the problem.
If it's more of a central sleep apnea, then I think only the CPAP machine would help (or if it comes due to some medication etc. then discontinuing it may solve the issue). Obstructive sleep apnea is more common though.
There are some pillows that you can buy, that are designed to keep you from sleeping on your back. And I think you could get some mouthpieces to give a try, if it's your tong falling to your throat, while you sleep on your back. Typically those mouthpieces are custom made by dentists, but for a cheaper solution to give a try, you can most likely find some cheaper ones 'from the shelf'.
I'd try one of those quick and easy remedies or consult a dr. or do both. To me the signs are there.
My .02 $