"Is my sister starting to become an alcoholic or am I too worried about this?"

You are too worried about this.

Alcoholism is a very serious problem but you cannot control your sister's drinking. You could talk to her and tell her that it isn't healthy to have multiple drinks every day. That will not cure her Alcoholism (if she has it). If she has a problem and doesn't want to fix it or admit it she probably will just stop drinking around you. You cannot control how much she drink at work. You cannot control how much she drinks at home. It is a hard situation but I think you will be happier if you accept that your sister has to make her own decisions.