Your symptoms definitely sound like Obstructive Sleep Apnea. Was wondering if you have contacted a sleep doc yet?
I will guess obstructive sleep apnea.
I took a simple, low cost (affordable if without insurance) at home overnight recording Oximeter (Blood oxygen saturation levels) test. The simple equipment was delivered to my home and picked up off my porch the next day when I telephoned to confirm the test was run. The results were made known to me in a few days (don't remember how many). In my case it showed periods of low oxygen levels, sufficient to qualify under Medicare (yes I have insurance) for supplemental oxygen. I discussed with my primary care doctor and ended taking an overnight sleep study at the local hospital (not low cost) and was diagnosed with mild obstructive sleep apnea... this suggested use of a CPAP breathing mask, but I declined saying I wanted to lose a little weight, was not much overweight but the sleep specialist agreed that even a little weight loss may open my throat a bit at night. I lost about 10% of my body weight and no long have the symptoms, I have not been retested.
Sleeping on you side, not back, may provide relief if you have mild OSA. Give it a try and consider discussing with your doctor, I suspect you have a physical not mental sleep problem.