Making one usb headset work with two computers
This won't work, and will not be a good idea for the PCs. 

USB 2.0 (the most commonly used at the moment) is a half duplex differential bus, which means that the host and device take it in turns to send/receive. The host (PC in your case) initiates all transactions, which means the device must wait for a signal from the host if it has data to send.  

If you have two hosts on the same bus, they will both be trying to send data at the same time and things will get very confused. Plus it may put undue stress on the output drivers, as they will be fighting against each other (known as bus contention) USB is quite tolerant of problems like this, so it's unlikely you have damaged anything.   

If you were comitted to doing this, you would probably have to design your own adapter (using a couple of microcontrollers, FTDI chips, or similar)  

Far easier is to go analogue as Chris suggests, this would only require a simple mixing circuit.
Or transmit audio data from one PC to the other, combine and then send to headset.  

EDIT - for an analogue mixing circuit:

For the microphone, you would hope that the internal amplifier might be low impedance enough to drive both PC inputs okay. However, many simple electret circuit are pretty high impedance, so you might want to use a simple opamp buffer:



The opamp can be another similar part, and the +9V can be less/more depending on what you have available. You might want to use the existing power from the PC (5V?) that powers the electret, and use a low voltage single rail opamp.
Before you try any of this, I'd just connect straight to each PC mic input and see if the quality is reasonable.  

The headphone drivers are the trickier part, these certainly need to be mixed properly, or they will attempt to drive each other. Something like this should work quite well:



This only shows one channel, you will have to duplicate for the other one. The grounds must be tied together also (not shown on schematic)
Depending on how big your headphones are, you may need to use something like an LM386, or you may be able to drive directly (especially if you pick a high current opamp)
Google for "LM386 headphone amp" and you will get overloaded with circuits.