UC Berkeley does spring admission (randomly) in the form of spring 2016 start, FPF, and Global Edge to ensure that there are students present the next semester to fill in the spaces for the students who graduate, drop out, or transfer after the fall semester. Instead of thinking that you barely made it under the wire, think of it as UC Berkeley doing all it can do to bring you in and get you to matriculate. If the school truly thought you were inferior, it always has the option to not pick you up. As for the matter of how your peers perceive you, I wouldn’t mind that one bit.
I stayed over at UC Berkeley for its OSP (Overnight Stay Program) and an RA there told me that no one barely remembers who was in FPF, Global Edge, or CC during the fall semester after a few weeks into the spring semester. If on the off chance that you do happen to meet a person with an inferiority complex and who gloats to you that you started in the spring whereas s/he started in the fall, you’ll probably realize that you’re better off not being in the presence of such a person.
Just join some orgs once you come in the spring and find your niche. Make some friends and the only thing that they’ll care about is not who you were, but who you are.