Yes, you can claim student loan interest paid in a prior year on the prior year tax return - by filing an amendment. Only interest paid IN 2016 is deducted on 2016 tax return.
If you filed prior years' tax returns with TT, please see link below for amending instructions.
https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed
If your haven't filed with TT - it is a little more complicated, as you would have to recreate your original in TT, then amend it.