<human>: Can you provide a brief overview of the text?

Me and my girlfriend have been dating for roughly a year and we just entered our first year of college. We are at schools more than a thousand miles apart but we're very committed to our relationship. I know your thinking I'm only 18 but this is a person I could see spending my future with. 
But anyway she's been having a tough time because she doesn't like her school. I've been having a good time and our relationship has been very strong. I've been starting to go to parties here I drink and get drunk and just generally have a good time.

The problem is every time I drink, my girlfriend gets mad because she thinks I'm going to cheat on her. I have never cheated on her or flirted with another girl. She tells me to just not drink for one weekend to show I care and I have done that but the next weekend came and the same fight erupted. Now she tells me to just not drink for one weekend but I keep telling her that that is not a solution to our problem. 

The bottom line is that if when I drink, she doesn't trust me and just gets mad at me. I really only drink once a week and it's always on a Saturday or Friday night. She sometimes goes out to parties but she doesn't really drink. 
So my question is how can make her trust me when I drink?
And obviously sobriety would be a solution but is that unfair of her to tell me not to drink?
<bot>: Long distance girlfriend thinks if I drink I'll be unfaithful. Not sure how to prove to her I won't be