I updated my iPhone 6S via the update section on the phone to ios 9.2.1. and now whenever I connect to itunes, it says a new update is available which is ios 9.2.1. Should I reupdate it? Maybe the one through the iphone wasn't complete.
I think you updated to 9.2.1 (13D15) on your phone. The new version, which is only available via iTunes, is 9.2.1 (13D20). It only fix the Error 53 that some people had when they upgraded/restored their phone if it has been repaired outside an Apple Store.
So don't worry, you can just leave it on the 13D15. Or you can upgrade to 13D20 if you want, it's up to you.
I noticed this yesterday having not connected my iPhone to my Mac for awhile for a backup and wondered the same. I totally forgot about the Error 53 drama.