Izzy had felt bad at first for going out after she had told Alec she wouldn't but people were getting hurt and even if he didn't think they could, Izzy knew they would be able to help. They were shadowhunters. She and Jace had been practising everyday and were confident in their skills.
They'd not gone far from the apartment, they hadn't needed to and they'd soon taken care of their first demon. Izzy's guilt had lessened after that.
She heard Clary the same time Jace did and had her whip in hand as the troll thing turned.