First, courts are loathe to enforce non-compete clauses because doing so may prevent people from obtaining gainful employment. In addition, to be enforceable, courts want to see narrowly tailored clauses (not "you can't work anywhere in this industry"), particularly if you did not hold a highly sensitive position at the company that granted you access to vital company confidential information.
Part of the "narrow tailoring" means taking a careful look at the time frame of the non-compete. The longer the time frame, the greater the justification the company will need to enforce it.
To get a clear read on your situation, consult with an employment attorney to review the actual language of the severance agreement.
Nina L. Kaufman, Esq. is an award-winning New York City attorney, edutainer and author. Under her Ask The Business Lawyer brand, she reaches thousands of entrepreneurs and small business owners with her legal services, professional speaking, information products, and LexAppeal weekly ezine. She also writes the Making It Legal blog.