Back Brakes grinding and squeaking

So I have a 2004 Chevy Cavalier. About a year ago maybe a little less my back brakes started grind when I brake. Its not a constant grind, it more like it is just grind in one spot as the tire turns and slows down. So I figured "hey I need to get my brakes changed." So I took it to Tires and Mufflers (i think that was the name) and they tell me that my brakes are fine. They just had alot of dust in them. He cleaned them out and I left... everything was fine on the way home. Next day the grinding starts again. So about two weeks later I look it to someone else. He changed my back brakes. They were fine for a couple days, then they started grinding again but now they are squeaking too. Unfornunately I work an hour away from home and by the time I get off it is too late to take the car to the mechinac, so about two monthes later, I take the car back and he cleans out my brakes because there is "dust" in there. Again I leave the place, go home, the next day they are grinding ago. As you can see this goes on for a while. The last time I took the car to him he changed the back breaks again, this time my brakes did not grind for a whole 3 weeks. (trust me it was exciting) Of course now they are doing it again. I am confused. Everyone keeps telling me there is "dust" or whatever in my brakes and then they change them. I do have to drive alot to work, but the car is not even lasting a day after I get them changed or fixed or cleaned! If anyone knows what is going on, it would be wonderful if you could give me cues, or anything that could help me. Thanks in advance!! =)

The dust they refer to is Brake dust and is common in rear brakes,fronts as well however the dust can escape easier. Do you know if they resuface /turn the brake drums when they put new brake shoes on car ? a cheaper brand of brake shoes could be part of the problem. how are the front brakes for wear? Back breaks usualy last longer than the fronts.

My front brakes are fine. They were changed too. I am pretty sure that drums were replaced. I will have to check with the mechniac. I read today somewhere else about the drums maybe being warpted.. which kinda made sense to me being as though it's not a constant grinding sound. Its more like a Chee Chee Chee Chee and there is a little more time between them as the car slows down more. Seems like there is one "Chee" every time the tires rotates one time around (180 degrees). I will have to check on if he put cheap brakes on there too. I would think so though he is a good friend of my boyfriend's family and they bring in ALOT of business for him. Also I should probably tell you a little more history about it as I forgot some details.
In December we went on vacation and a friend used my car. When she picked us up from the airport that is when it started making that noise. She swears that she did not hit anything. But I had to get new rims and tires because the front rims were bent and the tires became warpt because of that. The mechinac said it looked like she hit a curb or a speedbump going really fast. Before going on vacation my car was and had no major issues. (Gosh I miss those days)

I know what you`re saying about the possible warped drums. However I thought that to be the case with my `00 Sunfire so I changed the drums ,brake shoes were fine. I also did a complete front end brake job ,I still have at times the vibration when braking from highway speeds . So I would doubt if you have new drums on your car that they are warped,IMO. I would not be surprised if it is related to abs issues with these cars .

Do you know when you had your brakes done, did they replace the hardware when they replaced the shoes in the rear. I have a 2003 Cavalier that started doing the exact same thing in the rear after I changed my back brakes myself. I did not change the hardware which is making me believe that I should have, and I took my car to a mechanic at sears and he told me the exact same thing that it is the brake dust, he cleaned them and for a day they did not make that annoying noise and grab at a certain point when braking. But after that day it started right back up and it is pissing me off. I am going to replace everything and let you know how it all turns out. One last thing, is your car within alignment specs in the back because mine is not and that might have something to do with it as well.