Social Security Questions? Ask a Social Security Expert
If you are covered by Social Security you can certainly apply for benefits even while you work. You can apply at the Social Security Admininstration web site www.ssa.gov. Certain governments and their agencies have opted out of the Social Security system. If you work for one of those you will not be covered. To verify the inclusion of your coverage you can simply look at a recent pay stub. If you see a deduction for any of the following taxes (they are all different names for the same item) then you are covered:
If you are not covered you could apply to retire and receive your pension. Then find employment at another school if that suits your plans . There is no restriction against working while receiving Social Security retirement benefits.