My 3mo enjoys putting her fist in her mouth and chewing on her thumb. Is this part of her motor skills development, and should I pull her hand out from the mouth whenever I see her doing that? Sometimes, she will suck her fingers till she vomit as well. ?

Yes this is very normal and almost babies will attempt to suck their fingers or some other things. They are using their mouth to explore and secondly could also be baby is teething soon and need to soothe the gums. I will try to pull her hands out when she tries to suck and give her a teether. The downside of doing this is she will suck other things around her even when she is outside. But if you let her get into the habit of sucking fingers some babies will get hooked on it so much they will keep sucking fingers even when they are much older as it is harder to quit fingers. My niece suck hers till 6 yo! But if you are afraid she will suck other things which may not be as clean then fingers is better. Depends on your thinking. But not all babies are the same. For teether I love the Ange brand banana teether made in Korea :)

It's part of exploring their hands and fingers. I tried to pull it out and warn baby and even smack baby it it didn't work - maybe I didn't persist Long enough. My boy is 6 months now and he still does it. Waiting for him to out grow it. You can reduce it by giving them pacifier or other toys or soothers to chew on. My boy loves a chilled tether and a hard metal ring - so u can see for yourself how u wana handle it. Some people feel better to use soother for fear of next time hard to quit sucking hands and easier to quit soother (just don't give)

Yes, it is. She is exploring her self and developing motor skills and coordination and it is a way for her to self soothe. I generally don't pull her hand away, but I gave this wrist rattle for her instead as I also do fear that she may chew and injure her own finger! She outgrew this completely at around 8 months. https://www.amazon.com/Lamaze-Gardenbug-Wrist-Rattle-Finder/dp/B00R7Q2RVK Saw Mothercare Paragon selling this item as well.

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my girl does tht too! but I just let her be. I believe tht they will grow tired of their fingers if we don't stop them. its like, the more you want to stop them, the more they want to do it. (:

It is. They will put everything into their mouth for quite a Long while. They are learning, registering shapes, sizes, texture when they put things into their mouth.