Hearing a clicking noise coming from the driver side

I just purchased a 95 Buick Riviera. From what I was told that the engine was recently replaced with the same NA 3800 series 2. While driving the car home, I noticed when accelerating or if the car is slightly going uphill, I hear a clicking noice coming from the driver side. when the car is on a flat suface and not pressing on the gas to accelerate, the motor is a sleeper. I don't hear any knocking noise coming from the motor when idling. only when taking off from 20mph and up pressing on the gas pedal. I'm hoping its not a transmision problem because the car still runs smooth & has the power it's just the noise i'm worrying about. I'm not sure if im clear enough bout the problem. I'm also new to this site which I think is cool. if anyone have any ideas, please let me know before i spend unnecessary money. All your help is deeply apprieciated.

Sounds like a possible exhaust leak. Check the flanges on the crossover pipe, and also the downpipe for leaks.....

the 95 cast iron headers are notorious for cracking.mine have cracked again.thank god i invested in a welder. hold a piece of toilet tissue,and pass it along either side of the header and if it flutters ,that's a good sign that its leaking.that works for the front too,just be sure the fans aren't running.that's how i found mine......

Thanks for the response.
I will check my exhaust system for any possible leakage.
I have a video of the problem. As soon as I figured out how to post videos, i will post it. The sound seems to be coming out the driver side & it sounds like something thats slipping everytime I press on the gas to accelerate or when the car is on a not too steep hill.

I was able to post a video of the noise. Sorry for the wind blowing that its hard to hear the sound the car is making. listen to it when its @ 1:36 - 1:40 then @ 2:34 - 2:40. It doesn't sound like an engine problem to me.