You can claim all medical bills and health insurance premiums (including Obamacare) paid out-of-pocket as Medical Expenses in Schedule A - Itemized Deductions
Medical Expenses are subject to the 10% rule (or 7.5% if you are over 65) and you can only claim the excess over 10% (or 7.5%) of your Adjusted Gross Income.
Please note that Itemized Deductions will only "help" when they total more than your standard deduction.
For 2016, standard deductions are:
For a taxpayer under 65, not claimed as a dependent
In TurboTax, you can enter Medical expenses by following these steps: