That sounds weird. I suspect you've already been given the tip in the forums that you should try using a different keyboard and/or mouse. It's enough if a key is stuck somewhere, but you would certainly notice that outside of SL. At least I know it from gamepads
You can also check whether any scripts are active that trigger this.
In Firestorm, click on
World -> Area Search.
then click on the "Filter" tab
uncheck the "Attachment" box under "Exlude Objects".
check the box at the top ("Only list objects that are:") under "Attachment"
then go to the "Find" tab
under "Owner" enter your name, namely your display name
Then click on the Search button and all scripts that are currently active on and around you and belong to you will be displayed. If any of them seem strange to you because they don't match your surroundings (furniture, clothes, hair, etc.), try "Return". Hope that helps.
Other than that, all you can do is watch your Avi to see if she/he is secretly using any drugs Sorry, bad joke, no offense meant, but your problem sounds really weird. Maybe you can describe it in more detail. Does the problem occur immediately when you log in? Or only in certain places, e.g. well frequented places or something?