If you sleep in the same room as someone else, they'll be able to hear it, it may even wake them up. It sounds a bit like nails on a chalkboard, back and forth for many minutes at a time. Perhaps they'd be able to tell you how often you do it.
Bruxism is a common side effect of drugs/medication. Look into the side effects of what you are taking, and consider different drugs or ceasing consumption of those substances.
Some interesting approaches to treating bruxism are listed here:
http://www.wikidoc.org/index.php/Bruxism Personally I am fascinated by Dr. Nissani's approach and believe it is best understood as training the subconscious brain through psychological conditioning. I think the occlusive device is foolish as it would be a bulky life-long device and is not compatible with people with low salivary function or sleep apnea.
The low cost mouthguard may be your safest and cheapest bet.