On my Note 2 it would always be on 4G. The Note 3 is always on 3G and I am in the same area that I always have gotten 4G. I've gone into the network mode and tried Global and LTE/CDMA to no avail. Am I missing something?
I would ask your cellular provider for a new SIM card before you stress out too much. If that fails request a replacement. If you're within the 14 days and close to that ending just exchange it. A factory reset is another option but I don't know how much that would fix.