I'm so sorry this is all come tumbling down. I know you probably feel a little like Alice falling down the rabbit hole right about now. I know the situation you are in is tough, but I really think you need to find a new neurologist, one who specializes in migraines and/or daily chronic headaches. Your doctors should be working with you through this situation, not telling you to hold on for two months. Yes, it takes time for medicines to start working, but there are other things they can do to help you and there are other medicines you can take that will help you with the pain. Something like Migranal has been really popular and works pretty well and it is not a narcotic. I've been suffering with daily chronic headaches with migraine for almost 3 years now and one the best things I have learned is that you and your doctors are a team. If there is something you do not like, tell them. It also helps if you are able to take someone with you to the appointment to help stand up for you and also to keep you from overlooking things. When I first got sick, I was lucky enough to be able to have a friend to take to appointments so I wouldn't be overwhlemed.
Also, may I ask you where you live? Depending on where you live, you might have easy access to a headache clinic who are equip to handle people like us. But I really think you need to find a doctor that is willing to work with you as a team, and not just brushing you aside.
We are all here to help, so please keep asking questions and I know people will try to answer them the best they can. I hope you find some relief soon. Take care.