I can only see Incoming Messages
We have seen such issues when your device manufacturer or carrier enabled RCS by default. RCS is basically a new standard for sending rich media in the messages. Different vendor/carrier has different name for it. For example, AT&T and T-Mobile call it "Advanced Messaging". You can find more information about RCS here. https://en.wikipedia.org/wiki/Rich_Communication_Services
Currently Android does not have support for it. You have two choices. The first option is turn off Advanced Messaging in the default message app. You can find this option in the Settings of the messaging app. Here is a screen shot for a Samsung device on AT&T.
The second option is download some third party messaging app from Google Play and put the default messaging app in protected app. This is a better option if you think the user may change the Advanced messaging setting back to enabled. Because the third party messaging apps are not provided by your carrier so they don't support RCS. Here are just two apps out of many that you can try: