Yup, he's performing a gambit. What you need to work on is how you respond to opening plays. Your choice to develop king side knight (3. Nxa3 Nf6) was probably not the best decision, as rushing for the early castle doesn't accomplish much for you, and it doesn't make it much harder for him to attack you one way or another. Furthermore, that knight doesn't reinforce your defense, nor does it convey any sort of offense. It leaves your king's pawn unprotected, and only attacks an obviously terrible move from white to respond with king's pawn, which even a remotely competent novice wouldn't do in response. It lets him take the initiative again when he offers up his queen's pawn, since it removes your development of the center if you take it, and lets him develop in response regardless if you do take it with either his bishop starting a pin, or just taking your pawn for the trade with his queen. Either way, it gives up your defense of the center. Nf6 was his foothold back into control.