I like the idea of EFT to help you calm down about it - you wont be able to think or reason if you are totally freaked out.
Once you can get to a calm state of mind over the issue - I agree with Alyssa: do what you CAN to avoid contamination. But I would also do some research to see how they spread (will fumigation cause them to flee to safer ground?? like next door??) and I would DEFINITELY put it on the manager's responsibility to financially see that you are safe from insect infestation. Look up articles and see how other apartment complexes have responeded and present him with those. See how hotels have handled it, and present him with those articles. That way he can't try to 'cheap out' and only treat one room and hope for the best. No, it really needs to be dealt with properly - - whatever that is. You also might want to call some exterminators and ask their opinion of what the best way to handle the situation is, but don't YOU get the appt for the fumigation, make the manager do it. Just get the info and let him know you're on top of this and serious about it (and rational and level headed: he won't fund an apartment wide fumigation based on your fear of bugs, but he will if there are standards that he has to keep up).... might even call the city and see if they have safety codes/rules on how these things have to be handled to prevent a larger problem. The bug-guys might even know that, too.

Just my ideas.
But first start with calming down. Yes it's big, but not so big you can't handle it, not the end of the world, and not something you can't overcome. You can do this!!! You are a very strong and determined woman!