Your low oxygen levels are not caused by anxiety. You did not state whether the fall in oxygen saturation was while awake or asleep. If while asleep, you have a sleep
disorderAdjustment disorder
Anorexia nervosa
Asperger syndrome
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Bipolar disorder
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Chronic motor tic disorder. If while awake you most likely have a lung problem or conceivable a heart problem with shunting of blood. The low oxygen levels are most likely caused by the same disease that is causing you to experience shortness of
breathBreath alcohol test
Breath holding spell
Breath odor. You are correct that the normal response to a low oxygen levels, also called hypoxia, is to hyperventilate, breathing harder and faster. It is possible, but highly unlikely, that you have a problem with your respiratory drive, causing you to hypoventilate. This can easily be sorted out with a simple breathing test, called spirometry, a chest x-ray and measurement of arterial blood gases (ABGs).
Your doctors should be able to sort this out and discuss the likely causes of your shortness of breath. Perhaps this would be a good time to seek consultation with a lung specialist to check your lungs for blood clots or chronic obstructive pulmonary disease (COPD) and your heart for a defect that allows poorly oxygenated blood to be pumped to the rest of your body.
Do not delay.
Good luck.