If it does not work, you may have a glitch in the backup you had when you were using the old phone. When you restored the backup to the new phone, the glitch was also transferred as well.
To rid this, make a backup in iTunes...music, data, everything. Now restore the phone as a new device. Do NOT use the backup yet. Setup enough of your settings & info to test Messages. If the test is successful and you have no message issues, then you can choose to re-build the phone completely from this "bare state"...not easy.
If you now restore that newest backup you made, test the device and the device has the same "blank bubble" issue, you can bet that the backup has a botched/glitched setting somewhere.