If you have installed the SMS Magic Interact 1.45 or later version, you might be facing some issues with the duplicate records in the SMS conversation view when someone responds to your SMS. Which also means that the SMS which should be only listed in the Incoming part of the conversation is also displayed on the outgoing SMS section.
All you need to do is to check if you have installed the SMS Magic conversation View package in the past. To check this, go to Setup -> type "Installed packages" in the quick search box -> Look out for "SMS Magic Conversation View 1.0". The reason behind this behavior is that after the upgrade, you have an inbuilt conversation view package. Plus, if you have installed them in the past, you have 2 copies of the same package and hence the duplicate records.
If you find any entry for this package, all you need to do is uninstall the "SMS Magic Conversation View" package and your issue would be resolved.