Rep Power: 0

I drive this car daily, putting 30k miles since august, the car now has 208k. I've always stayed up on maitenence, and I've had no prior issues.
Yesterday morning, I started my car and it gave me a deep sound like a maxed out sub, prominent vibration, and a rattling coming from the passenger side that's not the blower motor. If i accelerate, the sounds fade, if i maintain speed it's a slight sound, but the second I let off the gas all the sounds are prominent again. - It's especially bad in lower gears/speeds. anywhere from 0-45mph, it'll make the sound no matter what. The car also seems to have a random shiver, and I noticed it's shifting a bit harder than usual. Also a notice in lower mpg.
So, i topped off my trans fluid, changed coil packs and threw new spark plugs in for the hell of it. It seemed to help a bit, until the car cooled off, and I got in it to drive it home. It seemed to be just as bad as before.
There are no leaks as well.

I was just curious on any suggestion on where to start digging, or any advice. I'm quite at a loss, as I'm still learning car's and this is my reliable daily.

 
Rep Power: 222

Check the heat shields and engine mounts