It sounds quite a lot like seperation anxiety. We had this with Rupert when he was young. I am sure there are behavioural experts who can help with this but we just gave him time to grow out of it, and he did within a few months.
Of course, before then he ate a door frame, rotted some floorboards through (He managed to find a nice tucked away area to do his business), ate superglue, terrorised the cat and ate one of my boots.
What we found that helped quite a bit was a good selection of toys and leaving some of our clothing for him to lie on (Or, in truth, eat).