Yes, you will be in trouble. Rules are more than clear:
On a J1 visa as a non-student you are a nonresident alien for the first 2 calendar years.
In your case year 2013 and 2014. Usually is always better to file jointly unless your wife was outside of the U.S making a lot of money, because her worldwide income is taxable, but she was unemployed so you should had file jointly to maximize your return. I will definitely go and talk with that company.
