I know I'm really late, but I thought I'd update you all. My cousin is a CPA and she helped me out with this. She basically reiterated what you guys said, that you just add the amounts from the various W2s.
Idk if I made it clear, but for most of what I do, we pay into a system called SERS, the School Employees' Retirement System. But we occasionally do outside work, for which we pay into social security.