Does severance delay my unemployment claim? after 14 years as a customer-service rep

My employer is paying severance in instalments and I am not sure whether to file now. It has been weighing on me all week. The agreement mentions a release and a payment schedule. Who should I ask before signing?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.