What could cause low oxygen levels after a carotid artery surgery and then hematoma removal surgery? dry esophagus from ventilator?

Lots of things: Low oxygen levels after a surgery can be caused by a large number of problems. Possibilities include ventilator associated pneumonia, pulmonary edema ( fluid in the lungs) adult respiratory distress syndrome, pulmonary embolism ( blood clot in the lung) so without more detail could not say. You should discuss with the doctors involved in the patients care. "dry" esophagus not a cause.

No: Aspiration or hospital-acquired pneumonia, pulmonary embolism, underlying lung disease would be some of the possibilities.

Low oxygen: Patients having carotid surgery are older. They may have a weaker heart. Extra IV fluid they get during surgery and if they had to go back for a second time to address a hematoma...May have built up on her and can lead to lower oxygen levels. The lungs get a wet and the oxygen can't get through as well. Some time and medications to gradually get that fluid off will help correct the problem.