What should I do about my hamster

I've had a hamster for about a week. He's fine. To socialize, I feed him by hand and pet him everyday. He'll take the food, but when he's done... He'll want to try my finger, too.

I'm as calm and gentle as possible... He's not scared... I've even tried washing my hands thorough before interacting with him. It doesn't work. So, what should I do.

Also, my cousin thinks he does that because he's teething. If this is true, what can I do to help him?

try offering him the food with one hand and then petting him with the other; if you think that using the same hand you just fed him with might be confusing him

otherwise, it just takes time-depending on your hamster it may take two or three months before the process of taming is complete

And-if you don't already (which I'm sure you do because you sound very responsible and loving to him), just give your hamster a variety of chew toys such as cardboard and untreated wood (toilet paper tubes and the wooden chew blocks they sell for hamsters are a cheap way to give your boy something to chew on); your hamster is not teething, however those few teeth that you see in the front will continue to grow his whole life so you will need to offer him chew toys for the rest of his life; so that he can keep his teeth short by chewing

here's a link to the ASPCA's website where there's an article on hamster care...the 16th paragraph discusses the need to chew for hamsters: