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Why is My text box is grey and covering up what I am typing?
Try force closing the messages app. If that does not work, reboot. You can also toggle the character counter or the subject field. These should fix the issue.
Do a backup on iTunes, restore as new. See if it happens again while it is restored as new. If it doesn't, restore from backup and you should be good. Doing this will give you a clean install of iOS 9.0.2.