My son is 3 months and is also doing the same thing-Although not until his hands are red. He's drooling too so I know that the teething process is beginning. It stinks because at this age he is not very good at holding objects and bringing them to his mouth. He is getting better everyday though. The more he puts his hands in his mouth the better he gets, as with rattles, toys,etc.
It may be fun for your little on to put her hands in her mouth because it is a new trick she is learning to do as well.
I bought this supposedly "top of the line" teether from Discovery Toys. It's made out of some kind of rubbery material that makes me think "if I had a toothache, I'd chew on it myself!" It has a great feel to it and has 4 different textures on it that are sure to be soothing for teething. It is also red which is a bold and interesting color for infants.
Like I said, he cannot hold stuff really well so I have yet to find out if this thing is as good as they claim. And of course, I'll have to wait until he cuts teeth to tell. Look online for a Discovery Toys consultant. It was kind of pricey for a teether-$10.00 But the consultant I bought this from says that parents and babies LOVE it. We'll see.