Yes - You can still use the Deluxe version of TurboTax.
You can deduct the mortgage interest as long as the mortgage is a secured debt on a qualified home in which you have an ownership interest. Whose name(s) appear on the 1098, yours and/or your girlfriends? If your girlfriend is the one making the mortgage payments, it seems like she should be the one to take the mortgage interest deduction.
Please see the following articles for more information on deducting home mortgage interest:
