I have been trying to find information about a bug that many others have been posting on apple discussion boards about. With my Verizon iPhone 5 (16gb), after a phone call my LTE shows download speeds but no upload speeds. Browsing works fine but many apps that require uploads fail to connect. After consulting with apple on the phone and at the store, as well as Verizon on the phone and in store, there is still no information. In fact, apple points to the carrier, and the carrier points to apple. I know I'm not alone with this issue. In fact, a coworker of mine has the same exact issue.
The following steps have already been taken and have NOT resolved the issue.
Restored network settings.
Replaced SIM card.
Complete OS restore.
Reconnecting phone to carrier network
The issue can be temporarily resolved by doing anything that turns off network settings and toggles it back on (toggling cellular data on/off or airplane mode on/off). It's will keep LTE uploads functioning until another phone call is received. One other important note, this connectivity issue does not seem to occur if you're only on 3G.
List of apps that don't work with this issue:
Uploading pics to Facebook, Instagram
FaceTime over the network.