If these were over the air updates (you didn't load a file into the phone, the carrier sent you one over the air), they're responsible for any damage the update might have caused. (Let's hope this isn't another S3 4.3 update debacle). Just bring the phone to the carrier's repair center (or store, if they don't maintain a repair center - AT&T and Verizon do, in some store within driving distance) and ask that they fix or replace it. You're responsible for having any important data backed up - it's always been that way in the computer industry, going back to IBM 709 days (1958), at least. If you haven't been backing up in the past, and there's something on that phone that you can't replace (and it's important), you sure will now.
(It's possible that they have a method of non--destructive reflashing. That will leave your data intact. Ask them before they reflash the phone. [Normally, reflashing leaves you with a phone the way it came out of the box.] It can be done - the file to do it for the AT&T Note 3 4.4.2 is posted on XDA [and that's a tough phone to get into] - so if they tell you it's not possible, it just means that they don't know how to do it, or the corporate office didn't think it necessary to supply their stores with a way of doing it.)