Yes, you can amend both 2015 and 2016 returns to change your filing status to married filing jointly.
Many married couples find it best to file jointly since that usually provides the larger refund and you don't have as much due in taxes.
You can see in more details here Is it better for a married couple to file jointly or separately? why it's better to file jointly. And you will find more details on why you’d want to file separately on that page as well.
When you file separately, your tax rate is higher and you won't get to claim these things:
