Kynon does this too, a few times he's stuck a finger too far and gagged. Don't think he's teething tho as he likes to suck his fist and think he's just exploring, babies use their mouths for this so could just be she's found her mouth, they like to taste things as well as touch, just keep her hands clean and offer toys to chew on like m2a suggested. I've found Kynon still prefers his hand tho as he hasn't learnt to hold a toy really yet!