If an iPhone has full bars (shows 4G or LTE) and can make/receive phone calls but cannot get to the Internet (via Safari or any other IP app), then it’s a routing issue. Out of many routing issues, it MAY be that your cellular provider is having problems. BUT if all other devices (e.g. your friends and family’s) devices are working, then it is probably a routing issue with YOUR phone only.
There are several ways to troubleshoot routing issues on your phone.
1) Simply quit every app by swiping them away and turn your phone completely off, then back on. This will clear the cache and your phone may request the cellular provider for an alternate route.
2) Settings > General > Reset > Reset Network Settings. This will wipe out all network settings in addition to the network cache. Your iPhone WILL request the cellular provider for routing information as if it was new out of the box.
Now, there is a setting that will INHIBIT the iPhone from renewing the routing information from the cell provider – Data Roaming. For some reason, if you have Data Roaming turned ON, the cache is repopulated with roaming routing information. You have to turn Data Roaming OFF while attempting the above.