You need a mixer. Putting it through the computer will make it laggy. The Y cable doesn't work like that. Trust me, I've tried. Now I have an Alto ZMX52 on my desk. Works great. Wasn't super expensive. $50 on amazon. But you also need cables to go with it which are not standard headphone jacks. They's 1/4" jacks (like the one for electric guitars and professional audio equipment in general) so you'll need to buy a few of those. I bought a bunch of 3.5mm jack to 1/4" jack adapters as well as some other things to make it work. Since the mixer has a seperate 1/4" jack for each channel (left/right for both channel 1 and two as well as the output) you need 3 dual mono to stereo 1/4" jack plugs, as well as 3 1/4" plug to 3.5mm plug (headphone) adapter if you want to use normal aux cables.
Actually, this looks like it'd work. You'd need 3 of them. This mixer will give you a chance to merge 2 audio sources (and 1 microphone source). I'm not exactly sure how the microphone source works, and I don't think it works with typical PC microphones. (I tried). You can also put an audio source on the aux in which will play over... everything. So technically you can merge 3 sources + one microphone.