If you have lost your recovery key then unfortunately there is nothing to do, it can be regenerated but that will cause all data in sync to be deleted. You could try syncing your phone, then disconnecting it from sync, create a new sync account and connect your phone to send the data to that account, but there is a potential for the data to be lost there as well. sorry.
Directly recover SMS from Android Mobile Phone, you must to use a 3rd data recovery for Android.
Android Data Recovery Software is powerful that directly recover deleted or lost SMS text messages due to delete or format the SD card, restoring factory settings, etc from Android. This software support most of Android phones and tablets like Samsung, HTC, LG, Motorola, Sony,Huawei, ZTE, ect and keep data on your device original, no risk, deletion, modification or personal information leaking.