First thing to do is seek counseling. Seriously.

If you are really in tears over this, you have much worse issues that you need to work out. The door alone is not the only thing doing this to you.

Second, fix the door. If it's effecting you so much, just do something about it. Take a picture of the door closer and post it on the carpenter's forum, they'll tell you whether it's adjustable (and how to adjust it if it is) or if you need some type of silencer, etc.

Why would you move before you've attempted to remedy the situation? Mgmt can't know the door is malfunctioning again/still until either they catch it personally or someone tells them. Can you just place a call to get maintenance back out to fix it? Or perhaps type a letter describing what happens, have neighbors sign as well, and drop it off?

Tend to agree with fotostat's last paragraph if you're at your wits end and they won't do something soon enough. It's probably just a matter of tweaking the closing mechanism with a screwdriver to slow the speed the door closes.

To the OP: I would try contacting management. moonshadow does have a good suggestion with a letter.

I too find myself very shaken due to my neighbors door slamming. It startles you. And yes, we've had art work fall down because of it. (However, my neighbor does it on purpose not because of a maintenance issue.)

Best of luck