Yes, TurboTax can be used to amend your 2015 return. You'll just need the 2015 CD/Download version of the software in order to amend it.
If you filed your 2015 return with TurboTax, go here How do I Amend a 2015 Return Originally Filed with TurboTax Online? and follow those steps.
If you did not file your 2015 return with TurboTax, go here Buy 2015 CD/Download Software to purchase the download of the software.
Once you have that software installed on your computer and a copy of your original 2015 return in hand, go here How do I Amend a 2015 Return in the TurboTax CD/Download Software? for steps to amend that return.
Keep in mind, this return will have to be printed and mailed as well. Prior year nor amended returns can be e-filed per IRS regulation.
You will want to include any W-2s or 1099 forms that have federal tax withheld, if you made any changes to those sections. Basically, any new information that you entered, you want to attach copies of those documents to support your changes.
If you go here Instructions for 1040X and read under the Assembling Your Return section on the bottom of Page 13, it will list everything you need to send along with Form 1040X. There should be a Filing Instructions page that should print with details on what else to include with that 1040x return. And you may want to consider sending it certified mail so that you know when they receive it. And be sure to sign it.