DO NOT DRINK ON THE MEDICATION.
I tried a benzo taper at home, I just drank on top of it and ended up worse.
Eventually I did supervised inpatient detox and rehab. It was the only thing that worked, as I was extremely sick from alcohol and sleeping pill addiction at the point of quitting.
Keep close to SR if you don't have a local support system, that's what we're here for.
And it's far scarier if you DON'T stop.