I had enough medical expenses in 2017 to qualify for a refund, but only paid for a portion of them myself and the rest was covered by family. How do I answer this?

To claim a medical expense as a tax deduction, you must have paid for the expense yourself. 

If the medical bill was paid directly by another family member on your behalf, then you would not be able to claim that as a deduction.  If you do not believe that you paid enough of the expenses yourself to be able to get a tax benefit, then you do not need to enter any information into your return.  TurboTax will give you guidance about the threshold that must be met in order to generate a possible medical expense deduction. 

One other thing to consider is that medical expenses on their own would not be a tax deduction.  You must also be claiming other expenses that are reported on Schedule A Itemized Deductions.  This includes things such as mortgage interest, property taxes, and charitable contributions.  If you are not claiming other itemized deductions such that they are greater than your standard deduction, then you do not need to worry about trying to determine the amount of the medical expenses that you paid yourself.