I think the only practical advice anyone can give you is psychological - "Don't care so much." This might sound like its "too easy" or "won't work" or "not practical" but that's about as simple as it gets. That's what it boils down to. If you cannot do any physical activities to help you heal from this, such as yoga, meditation or reading a book, then the only other way to approach this is psychological.
I have social anxiety and I was talking to my sister about this the other day and she said "Eventually you're going to just stop giving a ***** so you might as well stop giving a ***** right now." The same applies to both of these situations, with your separation anxiety and my social anxiety. You are putting way too much emphasis on this disorder and on other people, and in my case so am I. I'm going to stop saying I have a social anxiety disorder because just by saying that, I'm already giving it power over me and assuming it is completely out of my control - and what can you do with anything that isn't in your control? Nothing. So take the reins or suffer, that's basically what it comes down to.