Yes, if all of the Qualifying Child rules are met you can amend
your 2015 and 2016 tax returns to add your dependent.
To be a Qualifying Child -
1. The child must be
your son, daughter, stepchild, foster child, brother, sister, half brother,
half sister, stepbrother, stepsister, or a descendant of any of them.
2. The child must be
(a) under age 19 at the end of the year, (b) under age 24 at the end of the
year and a full-time student or (c) any age and permanently and totally
disabled.
3. The child must
have lived with you for more than half of the year. Temporary absences while
away at college are considered living with you.
4. The child must
not have provided more than half of his or her own support for the year.
5. If the child
meets the rules to be a qualifying child of more than one person, you must be
the person entitled to claim the child as a qualifying child.
6. The child must be
a U.S. citizen or U.S., Canada or Mexico resident for some portion of the year.
7. The child must be
younger than you unless disabled.
For more
instructions on filing an amended return:
https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed?jump_to=answer_3288565
For more information
about Qualifying Child: https://www.irs.gov/newsroom/a-qualifying-child
For more information
about claiming a dependent on your
return: https://turbotax.intuit.com/tax-tips/family/rules-for-claiming-a-dependent-on-your-tax-return/L8LODbx94