Ok. First of all let me say that no, I didn't put the caliper back in a way where both pads are on one side of the rotor...I know I'm dumb, but I'm not that dumb. But thanks for all of your concerns.
Here are a couple of pictures of the problem I described above. As you can see, some of the material in the back of the pads has fallen leaving behind bare metal...I think I've discovered the problem, but first, let me show you the pictures I took.
Now let me tell you about the real problem. I discovered the caliper was shaking kind of bad. That's because the caliper is missing a little piece of rubber I took out by accident when I first got it. I haven't been able to find it. And to "solve" the problem i've been putting paper or something instead of the rubber thing. It has never caused a problem before.
Then I remembered the noise problem came after it stopped raining here in L.A. That probably happened because the paper I put got wet and became loose. That might have caused the pads to "shake" a little against the piston. Causing them to loose some material from the back in the long run and wearing off the anti-noise goo sooner than expected. Now two more questions.
1. What's the proper name of this rubber thing?
2. Where can I buy it at? (I'm fine if I have to buy it on-line)
Here's a picture of the rubber thing I'm talking about. Its the one with the big red arrow pointing at it.