On a J1 visa as a non-student you are a nonresident alien for the first 2 calendar years, so 2013 and 2014. After that you use the substantial presence test to determine residency status. So generally, if you were in the US the entire time, you most likely were a resident alien already for 2015 and will need to amend your return.
So for 2016 you can file as resident aliens, jointly and claiming your son.
