First of all, it is not beside the point that you work at home! That is your number one validation for being so upset! Also, your upstairs neighbor is not the nuisance, the squeaky floor is!!
Yes, it is management's problem. It is their building, their floor and their responsibility to keep it in the best condition possible. This is why you pay rent!! They need to have a professional come in and evaluate the floor and fix the underlying problems that are causing the squeaking.
If you've tried speaking to the landlords/management reasonably and have gotten nowhere, I suggest you go to your local court house and speak with one of the clerks in the civil division about putting your rent into an escrow account. From there you can inform your landlords, in writing, that you are putting your rent into an escrow account where it will sit until they fix the squeaky floor issue. You cannot be evicted for this and they cannot retaliate against you for this. The clerks should be able to help you as far as what forms you will need to file and how their process works. Beyond that, talking to a lawyer would help you tremendously. You do have rights as a tenant!
Best of luck to you!