No, you should not need to create a new tax class, you just need to be sure the tax class is assigned to your test product and to the local tax.

The debugging info will show up in the checkout area above the cart total summary, but it will only show if the local sales tax is actually being applied.

I'm not sure what else to suggest at this point. If you would like I could take a look at the admin settings. If that's what you would like to do you can PM me with log-in info.

LadyHLG