Can I deduct a previous year's medical expenses on this year's taxes?
No, you can only deduct medical expenses for the tax year in which they were paid. For example, medical expenses incurred during 2015 can only be deducted on your 2015 tax return.
If you weren't required to file a tax return in the year you paid the expenses, that deduction is lost; you can't carry it forward to a future tax year.
If you forgot to claim deductible medical expenses for tax years 2013 through 2015, you can always amend those returns to include the expenses. It's no longer possible to amend 2012 or earlier returns.