Does severance delay my unemployment claim? - any advice?

My employer is paying severance in instalments and I am not sure whether to file now. There are 18 people counting on me, so I am trying to be careful. I have a mortgage and need to plan. Who should I ask before signing?

Thanks for writing this out. I went through something close to it 6 months ago, and it got easier once I kept a simple log of every call and form.