Sorry for the troubles. Did you happen to try Resetting All Settings?
Likewise, did you happen to remove all the numbers in Settings > Phone > Blocked Callers? That may still be worth a test, even though your contacts are not in there.
Otherwise, yes, it may be a good idea to backup/erase and restore a fresh copy of iOS using a computer.
If it’s in fact an iOS issue and not a carrier issue, this should give you the answer.
I would typically set it up without restoring from a backup, just as a test. Because chances are if it continues it’s a carrier issue, and may require a new SIM card, or an adjustment on the account side.
Its unlikely this is a hardware issue, as this issue is normally not, and considering the same happened with your previous phone. So should be an issue with the software or carrier, but have been suprised before.
But before all that, I’d definitely reset all settings, which may just fix the problem, hopefully!
Restore your iPhone, iPad, or iPod to factory settings:
https://support.apple.com/en-us/HT201252