I'm going to tell you something that might not make proper sense right now, but will when you get sober for a while again. Getting caught-up thinking about your "new low" and having it reply over and over in your head is only going to enable you to keep the habit going.
inability to accept new low -> anxiety/sadness/self-loathing -> breaking point -> medication (possibly with additional "new low") - > repeat
This is a horrible loop in which to be stuck, but the reality is that it's something that addicts go through when things start to fall apart.
So you need to accept it and be able to break that cycle by not letting it corrupt your thinking to the point where you need a drink to escape. How is this done? I, and I think a lot of people will agree, feel that sharing embarrassing things with other people is a good way to go about it. Often a lot of the guilt is because you feel like you are the only one who has stooped that low.
I've never drank mouthwash, no, but I did do some stupid stuff in my drunken past life. Let's see...I've accepted drinks from women and men who probably wanted to get me drunk, just so I could drink for free on another's tab (though this only led to sex one time with one of my female friends). I've drank before important events, including my thesis defense. Umm there's more, but I don't feel like going through the complete list now. Point is, you're not alone and if I was in serious alcohol WD and mouthwash was the only thing that would make it stop, I don't know what I would have done.
What I notice is that you're only drinking mouthwash because you're adhering to this 3 drink rule. If you have the discipline to adhere to this, which you obviously do if you went for the mouthwash, then I think that you've got the discipline to give up drinking completely. A lot of people could never drink on a 3 per day rule, mouthwash or no mouthwash. Try and take this for what it is - a sign of strength.