am I unable to say I was a full-time student in 2020?
It depends. Were you enrolled as a full time student for the spring or summer semester in 2020 at a qualified institution? If so, then those months count also. Remember, the months do not have to be consecutive, and there's nothing I can find that says those five months must be at the same institution, or even the same program that will lead to a degree or credentialed certification.
