Check out the book Overcoming Binge Eating by Fariburn. It has helpful technical information about the various types of binge eating. I found it incredibly helpful.

My psychologist told me that I likely have bulimia since I had often fasted for extended periods of time to crudely counteract my binges.

Here is the definition from the Mayo Clinic...

"Bulimia (boo-LEE-me-uh) nervosa, commonly called bulimia, is a serious, potentially life-threatening eating disorder. People with bulimia may secretly binge — eating large amounts of food — and then purge, trying to get rid of the extra calories in an unhealthy way. For example, someone with bulimia may force vomiting or do excessive exercise. Sometimes people purge after eating only a small snack or a normal-size meal.

Bulimia can be categorized in two ways:

Purging bulimia. You regularly self-induce vomiting or misuse laxatives, diuretics or enemas after bingeing.
Nonpurging bulimia. You use other methods to rid yourself of calories and prevent weight gain, such as fasting, strict dieting or excessive exercise."

What you are describing is behavior that you should likely talk to a mental health professional about. I have found my therapist to be INCREDIBLY helpful in trying to understand why I behave the way I do. It is more than simply overeating for me. It is deeply rooted behavior that I have done for 20 years. I am finally starting to learn why and am able to begin treating the disease and not just the symptoms.

It is a big step to talk to anyone about it. You should be proud.