EMERGENCY - My Iguana is choking?

My iguana ate a stem from his collard greens and now I believe it is lodged in his throat. He is breathing but I can see it when he opens his mouth. I've called the emergency vet and they said we can either monitor him at home or bring him in but the vet is 45 min. away. I don't know what to do. At first he was a bit frantic and then he fell from his shelf (I caught him before he hit) but not he's seems calmer. I'm so scared. Do you think it's caught in his lungs at all? Should I take him to the vet?