Rim seems to be shedding metal chunks I have rim brakes on my mountain bike that's outfitted for urban duty.

Two weeks ago, I noticed that my rear brakes were weaker and louder than normal. I found that, although my pads still indicated 1/16" of wear left, the metal "internal" part of the brake had become exposed.

I immediately replaced the pads.

Since I installed the new pads, about every 40-50 miles I'll notice my brakes suddenly get noisy and weak. I'll get off my bike, and find a little metal chunk in one of my brake pads. After I dig it out, my brakes behave normally again.

I'm pretty sure that it's not from junk on the road. This never happens when I'm riding my other BSOs.

My rim looks and feels (to my finger) fine.

It seems like my rim is shedding metal bits. Is this the case? And, if so, what can I do to stop it? I've tried wiping my rim with a rag, but it hasn't made a difference.

Edit: I forgot to add that this is happening with both rims, not just the rear one that had the worn pad incident.
If you've used the brake pads up to the point where the metal is exposed, you've used them way too long and possibly caused some rim damage. There are wear indicator grooves on brake pads -- when they're gone, put on new pads. 

As for having metal embedded in the brake pads, I defer to this question. You might want to try switching pads (Promax stuff is generally low quality -- try Kool Stop), and checking the wear indicators on the rims.