Amy, I'm glad you are here with us this morning and are sober. I know you feel physically awful. Been there, done that. Way way way too many times to count.
Do you have benefits at this job? Sounds like you do if you are seeing the doctor. If you waver later in the day. If you start feeling worse, go to the ER and tell them you are withdrawing. Don't drink if you have this option. I know you're hurting.
In the meantime, you can call your health insurance provider and find out what coverage you have for outpatient. They can probably give you suggestions.
I'm sure you know this is a trick bag at the moment. You absolutely have to get sober regardless of the job. If you take the smaller risk of taking a few days for detox you stand a better chance of keeping this job than if you don't quit. You will be calling in more and more. Someone will report You've been drinking and that may be it.
I got talked to for smelling like alcohol at work a long time ago. I ended up in outpatient treatment. I'd had the job for a while so was fortunate that my supervisor was sympathetic and wanted to believe my story that it was heavy consumption from the night before. Be well.