I just bought some new sway bar links for my car. I had initially tightened them down well. I then found that one of them had fallen off , so I checked the other one and sure enough it was loose so I tightened it down very tight. The problem now is that after replacing the other side with a better part (passengers side), I'm getting a rattling and clunking coming from the drivers side (the one that is very tight).

I believe the noise is coming from the sway bar link on the drivers side because of it being too tight, is that possible????

You tighten them till the bushings swell to menthe size of the cups holding them. If they are loosening use a locking nut

I tightened them down so much that the metal bushing in the middle got sorta crushed.

well i took a crow bar and put it in b/w the sway bar and control arm , as I applied pressure on the sway bar, it starts to clunk/rattle. Therefore the piece of crap link needs to be replaced. Learned another lesson never buy cheap Chinese or Indian parts.