When I turn on my low beam headlights the high beam also goes on?
As long as you make sure you've tried turning off the high beam with the stalk, I would guess the stalk is the failing element. Does the high beam light on the dash, illuminate? If not, you may have another problem. Try wiggling the stalk and see if you can get them to turn off. Let me know once you've tried wiggling the stalk, if you can't get the highs to turn off. I hope this helps.