I would absolutely advise talking to a doctor about this. That very much sounds like an allergy, and although there are many meds that may help, none of us online can safely advise them for you, you really do need a prescriber with access to your medical records/bloodwork for that.
As far as first steps go, regularly taking OTC allergy meds and developing a daily cleaning schedule + filters for the bedroom + keeping your dog off the bed at the very least, and ideally out of the bedroom entirely, will help. Also frequently bathing your dog can help keep the dander down.
Cyberpunk dystopia at least has a good aesthetic…