If you shift-tab in skyrim special edition you can get your caps inverted. For people with a little LED showing if caps is on or off this can be particularly annoying. Luckily, there is a fix. Simply hold shift and type a letter. After you've done that the bug should be fixed. If you type without using shift your chat will be all-caps unless you press caps and de-activate it there, activating it everywhere else and also making your caps LED light up if you have one.

Edit: The bug probably happens when the game thinks you're holding shift, effectively inverting caps and obviously fixable by updating it by pressing shift.