When cough repeatedly the amount of fresh air taken in becomes less leading to fall in blood oxygen
It would have better if you had mentioned the results of all those tests including X rays and CT.
If your chest is fine then most probably you have sinus infection
causing your nose to block more so when you sleep. Same sinus infection cause dry cough
ENT examination is likely to elucidate more on this
Doxycycline is known to cause dizziness
So please consult an ENT specialist