Hello tennisgal2013,
It would impossible to write a text message with the behavior you are experiencing in Messages on your iPhone, so I definitely understand your concern with this issue. I'm not sure if you have tried this, but I recommend first trying to restart your iPhone and then a reset if the restart doesn't work:
iPhone, iPad, iPod touch: Turning off and on (restarting) and resetting
http://support.apple.com/kb/HT1430
If the issue persists after the reset, I recommend restoring your iPhone. You can find steps for backing up and restoring your iPhone in the following links:
iOS: How to back up
http://support.apple.com/kb/HT1766
iTunes: Restoring iOS software
http://support.apple.com/kb/HT1414
Thank you for posting in the Apple Support Communities.
Best,
Sheila M.