When you file your unemployment claim make sure that you document everything that you have mentioned here in detail.
I worked for Unemployment here in Colorado, and we are also an "at will" state, but it does matter on your claim the reason you are no longer working. If it was due to a "layoff", then you would be eligible for unemployment. If it's due to you quitting or being fired, then you may not receive anything.
What typically happens is that you are given an opportunity to say why you are no longer working, and your employer is also given that same opportunity. If both parties label it a layoff, then benefits typically are awarded fairly quickly. However, it doesn't sound like your employer is going to play nice and label this a layoff and you may have to fight it and go through the appeals process. Good luck to you!!