Yes, take action on this. I think you may have a slight penalty time but you will eventually get assistance. It sounds like you work for the printing company I did years ago, here in NJ. Please PM me with the name, I'm really curius to see if it's them. I too "technically" quit. I eventually had an arbitration meeting with unemployment and everything was going my way until they asked for former employer if they would take me back. He said yes and then I was asked if I would go back. My reply was basically, "you heard everything I said, I can't go back". "Well, since you technically refused employment, you are not entitalled to benefits."
I was still better off leaving, the best move I ever made. So I left the unemplyment office, walked down the block, and got another job, literally. It was good because at the time I was in a computer tech school (3 months from completion) and got a tech job that lasted almost 11 years (that's a lifetime for IT). But, as you know in Jersey, all Banks must be sold sooner or later, and so was mine. I have been unemployed for about 5 weeks now.
I know it's of little consolation but, don't get streesed, it's not worth it, and don't give them satisfation of knowing they've won.
And yes, I know how heavy paper is. Unloading trucks, loading machines, and cutting pallet after pallet of paper will kill you.