Can I get worms from eating an egg from a chicken that has worms?

I got my own chickens about a month ago and have been eating their eggs...I noticed today that some of their droppings have worms in them. My concern is my family getting worms from eating their eggs. What I want to know is if worms can be passed into the egg? Also another question, when I worm them, can I still eat the egg while the hen is being treated?