Hi there,
I think your doctor is referring to Macrocytosis which can be Megaloblastic or Non-Megaloblastic. Megaloblastic is usually caused by vitamin B12 and/or folate deficiency (as Taz2 says), but Non-Megaloblastic is related to liver issues, which seems to be the case. Quoting Medscape website
'Diagnostic Considerations
Diagnosis of the etiology of macrocytosis is required to guide treatment and determine the patient's prognosis. No complications are directly attributable to the increased size of the red cell; complications are attributed to the condition causing the macrocytosis. Failure to diagnose and treat the cause of the macrocytosis is a medicolegal pitfall. In addition to the conditions listed in the differential diagnosis, liver disease should also be considered.
Macrocytosis of liver disease is secondary to increased cholesterol and phospholipids deposited on membranes of circulating erythrocytes. This deposition effectively increases the surface area of the erythrocyte.'
If your liver function results show abnormal results I guess that's the cause for the 'fat' blood cells. Good thing is that liver issues can be caused by the painkillers you have been taking and as long as you give your body a rest from these drugs (ask your dentist for a liver-friendly painkiller) your liver will be able to regain proper function. Alcohol is a no no, though. Another differential diagnosis is hypothyroidism, have you been checked for thyroid hormones recently?