The war has lasted days, not months
He probably hit 16 a few months after ko'ing Kakuza, giving him enough time to age from there to the end of the sage arc. He was most likely already 17 by the time he got on the boat, which was a ride that to 3-4 months. The first half of the war could have gone on for a year or so, leaving him at 18 years old at the time
Another thing is the war era has probably gone on for more than 6 months now... All the major fights probably took weeks but we didn't realize. Also notice the time shifting in the sky, from night to day.