As Solara has pointed out, if you go to your doctor saying "I want benzodiazepines", then alarm bells will be ringing, but I'm not sure that's the approach many people would go for.
However, if you see the doctor and explain your issues, the doctor may well prescribe a benzodiazepine. I know in the UK, they are (usually diazapam) prescribed to people using and abusing alcohol, who want to stop, in order to help the individual deal with both the alcohol withdrawal and the underlying anxiety surrounding the alcohol abuse. However, both you and your doctor would have to closely monitor your situation, because it would become easy to use both and add to your problems.
I hate to have to say this, but while you are using alcohol in this way, your progress in therapy will be hugely affected. It just doesn't work if you are using alcohol to numb the pain and hide from the emotions that therapy brings up. That's why therapy is so damn difficult. It brings up all these memories and emotions that we don't want to, or feel that we can't deal with. But if you ride it out, accept that you're going to feel completely dreadful while you process this stuff, and don't negatively react by using alcohol or some other unhealthy coping mechanism, then it does get easier.
Honestly, I think you have too much going on right now to be dealing with tough stuff in therapy. Don't underestimate how difficult therapy is. But for it to be successful, you kind of need not to be too stressed out by other things in your life. I think you are overloading yourself, and being too hard on yourself. I think you need some more stability before you continue dealing with tough stuff in therapy. Move house, get used to time alone, look at resolving your alcohol issues. Once you feel more settled, then deal with tough stuff in therapy. We can all only deal with so many things at once, trying to deal with so much is just setting yourself up for a fall. The alcohol use is a sure sign that everything is getting on top of you. It's just my opinion, but I think you just need to stop and take a breath.