Chino may have tapeworms...PLZ HELP!!!

So, I guess I didn't get Chino outside quick enough and he pooped on my living room floor (thank GOD for hardwoods). At any rate, this may have been a blessing because I was forced to look at his poop. His poop had rice (?!) in it which after further research I have determined to potentially be worms. I called the vet and he wants a sample. Now I am concerned because he has already been on his first visit to the vet and he did not diagnose him with fleas. I've never seen a flea but he has had one butt dragging episode, puked 1 time (undigested food), but outside of that appears to be totally happy and healthy. I am also concerned because I have a 5 year old and 2 year old whom are extremely affectionate with Chino...what to do??? I know I should bathe him in DAWN, but what is an easy way to determine whether or not he has fleas?? PLEASE HELP! Any info is greatly appreciated...