Welcome here. It was indeed Dushashan's son. His name was Shrutakarna.
Actually, after Abhimanyu's other weapons and chariot were all destroyed, he picked up a mace that was lying around and fought Shrutakarna, and this was just a duel b/w them. Both of them fell unconscious during the fight, but Shrutakarna was the first to recover. He brought his mace down on Abhimanyu's head killing him b4 the latter could recover.
Lakshmana was killed by Abhimanyu earlier in battle, which was what enraged Duryodhan and got him to demand that Abhimanyu be killed no matter how. Drona then came up w/ the idea of surrounding him and attacking. Karna broke his bow from behind, Drona killed his charioteer Sumitra, and other warriors destroyed his chariot and his other weapons, like sword & shield.
After killing Lakshmana, the last warrior Abhimanyu killed was Brihadbala, the ruler of Ayodhya and descendent of Kush.
As for Shrutakarna, he was later killed by Bhima, but I'd have to find out which day he was slain.
Anyway, congratulations. Next question is yours.