Do I have to sign separation agreement to get the previously promised 6 weeks of severance pay?

I was employed by a company in Arlington, TX for 1 year and 2 months. I received notification that I would be terminated as part of a restructure. However, after I was notified of the termination, I agreed to work 6 additional weeks to transition and was offered 6 weeks of severance at that time. The email from the company to me was "we can offer 6 weeks of work and 6 weeks of severance". There was no mention of a separation agreement. I have copies of this email.
Now that I have worked the 6 weeks they are wanting me to sign a severance agreement in order to be paid the 6 weeks of severance, but the agreement was never mentioned prior to this time. Do they owe me the 6 weeks severance payout even if I don't sign the separation agreement?
Thanks