Separation anxiety in my puppy?

just last sunday we got a new puppy. he's a border collie/basset hound. he is also 7 wks (btw i asked my vet if 7 wks was too young N she said it's fine as long as the mom has weaned him N the owner said she did) but i think he has separation anxiety cuz if im not in the room wit him he will cry, bark, N howl until i come to him. he also wont eat unless i stand rite there (but thats cuz his original owner wud watch him as he ate). all nite he howls N barks N even tho we're in the other room we can hear him. i dont know how to make it stop. he also gets so upset that he spills his food N water N gets it everywhere. i keep him in the kitchen in a pretty big puppy pen. but we're getting so frustrated, we dont know wat to do. he also follows us everywhere we go N if he loses sight of us he crys. pls help!