My fiance filed the 1098 on her tax return and reported the property taxes on her tax return. Do I need to report the property taxes on my return, too?

No.  You can't both take the same deductions for mortgage interest or property taxes.  You can't both take the same deductions for any expenses...;)  

No.

 

Unmarried couples claiming mortgage interest and property tax

 

 You pretty much have a choice. One can claim it all or you can split it. It's usually best if only one claims it, allowing the other to use the standard deduction.

You have to meet the rules, which are:

1. You are legally obligated to pay it
2. You actually pay it. Paying from a joint account where you made sufficient deposits to cover the payments will usually meet this standard. However. paying from your own account would be a stronger audit defense.