my 2.5 mo old...

My 2.5 mo old daughter has been going to town on her fingers and fist lately hardcore.. Is that normal for babies her age my family says shes teething but I just think shes discovering her hands & my husbands family thinks shes hungry and i starve her which she eats 4-6 oz every 2-3 hrs. I've never seen a baby teeth before four months and she doesn't have any other symptoms like fussiness...but she just sits their and tries to fit her whole fist in her mouth and sucks really hard and loud