Caught drinking on the job

For preface, I know that this sound horrible, because it is. If you are here to judge, please just move on to the next post. Also this is my first post ever. But to get into things, I probably have an alcohol problem. I’m 22 years old and a manager at the restaurant I work at. I’ve been there since I was in my teens and have since then garnered an immense amount of trust within the restaurant. It’s a small family owned location, so there isn’t any corporate or anything like that. But the girl that I was working with later in my shift apparently told my boss and her parents that I was intoxicated on the job. I got a heads up from a good friend of mine that also works at my job and I was spiraling for the entirety of the morning. I literally woke up to his call and he was just telling me to expect a sit down etc. My boss did eventually reach out to me and ask if I was available to have a meeting. And I was just like crapppppp, I really screwed up. As someone who carries them self in a certain way and likes to have a certain image about themselves, this wrecked me. Anyways, I get to the meeting and I tell them what was going on. I was out very late the night before and had came to work hungover and still a little drunk. The look on the owners face and the general matter was very disappointing, and I honestly just feel like shit about the whole thing. The girl is only 15 who told on me so I can’t be upset. But we talked at the meeting and ended everything off with hugs. They said that they would get back to me and let me know how they’d like to proceed and even suggested time off. which I can’t really afford to do, but it might just be the best thing for me at the moment. I’ve been extremely nervous the entire day as to what they might say, but at the end of the day it is my mistake and I’m owning that. They were both very understanding at the meeting but obviously upset as well. It’s just not something a manager should be doing. The girls parents want me gone basically, which I understand. But I wish that they could just understand that my alcoholism isn’t the full picture of my life. I’m in college, educated, and just have a lot on my plate and made a very bad lapse of judgement. I also don’t know what I’m even going to tell my girlfriend or my family if the situation comes to light. I’m pretty sure tbh eh are just going to give me some time off to work on myself which I need and I’m so grateful that they even considered that. but my position and job are obviously still in the air. Any advice?