I think the perfect thing for you to do is to see a sleep specialist and have a sleep apnea test!
Pulmonologists are sometimes trained as sleep specialists and it might be useful to find one for MG reasons too.
Wow, that's really showing a common prejudice!
Body habitus is only one thing that can cause sleep apnea! And some people who are overweight don't even have it. AND skinny people can have sleep apnea too. There are things like a deviated septum or other anatomical obstructions that can cause it. There's also "central" sleep apnea which is caused by damage in the brain.
The problem is that you can't hear what you sound like when you're sleeping, which is another reason to have a sleep study. You can also ask that they check your O2 while sleeping, which some places don't do.
Do you tense up when you sleep? Some MGers do and are astonished why they are weaker after sleeping. Sleeping normally makes us relatively stronger. There are a lot of things that can cause a headache. Do you have a good pillow that supports your neck?
I hope you'll find a doctor to discuss this with. A lack of oxygen while you sleep is not a good thing!