If my 1099-SA only shows what I spent in 2016, but I spent in 2017 on 2016 bills, can I add them?

[DanielV01]

No, simply report the expenses you paid in 2016 for 2016 on Form 8889.  When you do the 2017 tax return in 2018, you will report the medical expenses from your 2017 distribution then.

Even if you had to change health insurance and no longer have an HDHP (High-Deductible Health Plan, which are the only plans that are HSA eligible), you still may pay for qualified unreimbursed medical expenses with your HSA funds.  If this is your situation, however, do not make any additional contributions this year as this would be penalized.  (You can, however, make contributions until April 18, 2017 for the 2016 tax year, if you have not reached your contribution limit).