Sleep Apnea Support Group
Sleep apnea is a common sleep disorder characterized by brief interruptions of breathing during sleep. People with sleep apnea partially awaken as they struggle to breathe, but in the morning they may not be aware of sleep disturbances.

I don't have hypothyroidism, but it seems to me that she should give you a prescription for a thyroid med regardless of treated sleep apnea or not.
Yes, depression is very common with sleep apnea, but it's common with many diseases, hypothyroidism included.
If you feel confident in this doctor then trust her and continue to go with her recommendations, but if you are doubting her in any way perhaps it wouldn't hurt to seek a second opinion.
Most machines are sooo quiet they can't be heard at all, even with someone sleeping right next to you. My partner, the first time she slept over admitted she was "frightened by it" because she had never seen anyone using one. So maybe the solution is to explain this to your man, and if need be, show him the machine and how you look with it on when you sleep.
As for love making, it never had any negative effect for us. In fact if anything, I was rested enough to WANT to make love. If your man is going to judge you based on how you look with the mask...or such, then I'd have to say, he's not worth having around, Once my honey got over her fear of it, she sort of liked the idea that it was keeping me safe, told me it had no effect on how she saw me....
hope it works out for you. But i Have to tell you....not using your cpap, could eventually lead to stroke. So think about the consequences of worrying about "beauty" over health. Love making will be fine...you will be great...if you just worry about your health and wear the mask!