I don't know what the medical definition of an alcoholic is, but I'll tell you my definition: an alcoholic is someone where the alcohol controls them, instead of them controlling the alcohol. If your mom is unable to drink without drinking herself to the point of drunk, then the alcohol is controlling her. Going weeks without drinking, only to tie one on, is called binge drinking and is a form of alcoholism.
You didn't cause her to be this way, you can't control her behaviors and you can't cure her behaviors. You can take care of YOU. Keep posting here, or "next door" in the friends and family section.
Both of my parents are alcoholics. Both are getting worse. There may be a point soon where I have to wash my hands of them and walk away to maintain my own sanity. My dad used to drink like your mom does. Then he retired. He now drinks himself stupid nearly every night, and many nights he drinks to the point of blacking out. My mom has entered late stage alcoholism and dementia. I can't change them - if they are making me crazy, then I need to take care of myself first.
I hope you find this helpful.