Sweating is not a sign of oxygen desaturation. There are many causes of excessive and/or seemingly inappropriate
sweatingSweating
Sweating - absent, many of which are
benignBenign ear cyst or tumor
Benign positional vertigo; not an indication of a disease state. Excessive
sweatingSweating
Sweating - absent can be
systemicSystemic lupus erythematosus
Systemic lupus erythematosus rash on the face, such as whole body
sweatingSweating
Sweating - absent, or localized sweating, such as yours, or as another example sweating of just one side of one's face. In the former group, of generalized increase in sweating are diseases such as diabetes, neurologic diseases such as Parkinson's disease and metabolic diseases such as tumors of the adrenal gland, called pheochromocytoma. In the localized group are many neurologic diseases of the brain and tumors or other causes of compression of the spinal cord.
If your sweating really is localized to an area "over the top of" your lungs, you should see a neurologist to see if the cause of the sweating can be localized to a particular place in your nervous system.
Good luck.