The medical expense tax credit is a non-refundable tax credit that you can use to reduce the tax that you paid or may have to pay. It can’t be used to generate or increase a refund. So, if you don’t have any taxes payable, you will not get the credit.  

As your wife’s income is $0, she will not have any taxes owning, so the medical expenses should be claimed by you.

Medical expenses can be claimed in a 12-month period with the final month ending in the tax year you are filing. So, you may be able to claim your unused expenses next year, if you can’t use them this year.