If you do not touch her - say, by always holding your hands together behind your back, as one guy did in my presence for wholly different reasons - it would be equally apparent that you want to touch her. You will not be touching her, but your desire to touch her will be no less if not more apparent than it is now.

Can you not hang out with her but resort to writing (texts, emails, social network posts, etc.)? Then you will be out of trouble for sure. Phone calls, too, cannot involve touching. Skype. Google chat. Old-fashioned snail mail. Lots of options.