I had updated my Mac 3 days back from El Capitan to Sierra. I had dual boot(Ubuntu + OSX). Before the update it was working perfectly with default boot as Ubuntu and by pressing option key I had OSX booted. But after the update I cannot boot Ubuntu. I have important files in Ubuntu, please help me.
It's not clear from your question whether you were using rEFInd or not. If so, the problem is most likely that updating to macOS Sierra reset the rEFInd boot loader configuration.
The first thing to try is reinstalling rEFInd. Reading The rEFInd Boot Manager: Keeping rEFInd Booting may also be of interest.
If you aren't using rEFInd, please clarify this in your question.