Hi ImYY4U1,
There are a couple of points to your post that may be relevant to iron out to identify what could be causing the behavior you describe.
SMS messaging usually has a character limit before the message is converted to be an MMS for purposes of delivery via a cellular carrier. From your description it sounds like you could be reaching such a limit while typing.
To isolate this further, try sending a longer message to another iPhone user and note if the same thing occurs. If not, then that SMS to MMS conversion could be a factor.
MMS is also used to send picture and video messages to non-Apple devices. Do those work? If so, then MMS would appear to be operating and enabled.
One other consideration is that you may be typing and registering the characters but not seeing them on your device. Try sending one of these longer messages even if you don't see the text on your side and determine if the full message is delivered.
The results of these steps will help narrow down if you may need to toggle the MMS capabilities of your device or contact Apple Support for further investigation.
Regards.