He's just old enough to begin experiencing separation anxiety. He realizes now that he's a separate being from you, but he doesn't yet know that when you are out of sight, you still exist, or that you'll come back every time. This is downright terrifying for some babies, who know their mommy is the very center of their world.
Time and experience will gradually make a difference for him. You might be able to help it along by holding him happily and eagerly, without giving him a sense that you'd rather be doing something else. This bonding is important for him right now. You might also try wearing him in a sling to leave your hands free to do things. Talk to him constantly about what you are doing to enhance his verbal comprhension and sense of togetherness.
Then, when you do need to put him down, play some going-away, coming-back games. Peek-a-boo is a good starting place, and then begin to extend your "absences" by hiding behind furnishings or stepping out of the room. Tell him "I'll come back!" Then disappear very briefly and pop back where he can see you. This, along with snuggles and tickles and lots of laughter, will very likely help him gain reassurance that you will, indeed, come back. Begin to extend your out-of-sight time as he builds a tolerance for it.
Also, letting him fuss and cry for a bit won't hurt him. Sometimes you just need a break. His ability to tolerate frustration and disappointment will grow in coming months. As difficult as it is to tell out littles "no," sometimes it's necessary. A child who is never disappointed is probably not going to be a very resilient child.
It's also possible that your friend doesn't hold him anywhere near as much as he craves, and he may have built up quite a hunger for connection by the time he's with you.
This is normal, and it will pass. Once your little guy is toddling about and becoming more independent, you just might miss these days.