Separation anxiety is demonstrated by several things, centered on how the cat acts when you leave, when you're gone, and when you return. Here, your cat is a dog. You try to leave, and she runs to the door, crying, climbing at the wall, saying take me too!! She tries to sneak out the door and run with you to work. When you're gone, she cries, and destroys things she never does when you're around. And when you return, it's the biggest event of the world - all is right, because you are home!!
Flattering, but...not preferable. Your cat must be retrained, because it's causing her extreme stress every time you leave, she's destroying things, and you may not always be able to successfully chase her when she sneaks out. What can you do?
The first task is for the owner. Change *your* routine. We don't realize it, but we do the exact same things again and again every day. Your cat will figure out that when you put on shoes, turn off the TV, pick up your briefcase and grab your keys, you're on the way out. So, instead, do things out of order. Put your keys in your pocket a half hour before you're ready to leave. Put on your shoes right away after showering. When you aren't leaving, go put on your shoes, pick up your keys and bag - and walk back to the couch and sit down. This will help to break her of the patterned response.
The other part - the return home. When you walk in the door, ignore her for AT LEAST 20 minutes. She'll be mad. She'll meow, and roll around, and get under your feet - but this works. You have got to demonstrate that you coming home at the end of the day is as routine as breathing, that it's not a big, stressful event that we should celebrate. This is VERY important - you must absolutely ignore every effort of the cat. Their behavior will likely get worse before it gets better - as it was phrased to me, your cat is thinking, "well, when I did this before, I got a response - maybe if I try a little harder?" As hard as it is, you must not talk to, pet, or respond to the cat at this time.
Thunderstorm anxiety is one that doesn't seem such a big deal to owners, but puts cats under a lot of stress. Try desensitivity training. Buy a thunderstorm on CD or tape, and play it on a nice day. Start with the volume very low, and while it's on engage the cat in her favorite game, give her treats, and make her see it as a time when good things happen. Slowly increase the volume as you go - and expect setbacks. If she gets scared, just turn the volume down and start all over.
Another thing about this - and this is so important, in the context of any anxiety based behavior - do not reward her unknowingly. As owners, our first response is to comfort the animal, to crouch down under the bed, pet her, and say that it's all right. Unfortunately, what you've just done is reward her for being scared, and reinforced that hiding is the right thing to do when a thunderstorm hits. Oops. Instead, try to basically ignore her. Roll treats or toys by every now and then, talk normally, but don't give her positive feedback for hiding.
Obsessive Compulsive Disorder is unfortunately somewhat common. Many times it may be as simple as excessive grooming, but some cats maim and disfigure themselves as a result of it. It often will require medication if your cat is already or on their way toward hurting themselves. The medication can often be tapered later, and the cat just needs a break from the anxiety to get past the hurdle and stop hurting themselves. However, OCD often mimics allergies, so it is very important to work with your vet if you suspect this.
You need to notice if your pet engages in the behavior all the time; if you can interrupt or stop them; how soon they start again; if it has triggers - anything at all you notice about its onset or relief. This will help to rule out allergies and get to the cause of the problem, and also may help you to remove the triggers for your cat.