Welcome to the forum!
Yes, a y-adapter like that would work for you. One thing to note with that type of connection is that both sources (PS3 audio via the monitor and the PC audio) would be feeding to the speakers - so you'd get distorted sound if both were sending a signal at the same time.
If your PC has an audio input, then you could feed the audio from the PS3 (via the Dell monitor) to that input, and then you'd just have one connection to your speakers. You'd just need to select that input on your PC when you were using the PS3.
Another option is a switch box. You can get one that has 3.5mm jack inputs and output like the MK-1 at the site
here (I've never heard of that site, so I'm not endorsing it). You can also get a more common switch box made for RCA jacks (like
this) and use cables that convert 3.5mm jacks to RCA (like
these).
Those are just a few thoughts.