97 Cavalier sounds like gravel in undercarriage

just started today, there's been NO noise before this. backing out of the driveway, I thought I was dragging something underneath my car. I stop in the street, get out to look, and nothing there. I drive down to the end of my block, brake, and it sounds like gravel in my undercarriage. the sound continues until I get up to speed, then starts again when I hit my brakes. I'm honestly afraid to drive this car right now with my 2 year old in it, so I can't take it to the mechanic until the weekend. I just need this car to last me til the fall, but I'm not going to pay for another expensive repair on it. Any ideas of what it might be? The brakes are more than 3 years old and have less than 10,000 miles on them, I hardly ever drive this car anymore. Thanks for any help!
A low use car can get rusty brake rotors quickly and can take a few stops and they usually clear up. If bad enough sounds and perhaps pulsing in brake pedal will persist.

The caliper may not be retracting well or have a cracked brake lining/pad -- must remove to verify that.

A bad bearing can do this too but will be regular at times and will not get better on it's own. Sealed up unit must be replaced if so,
 

I agree with Tom that it might be rust build up and if the noise is coming more from the rear of the car; it might be the brake drum that needs to be cleaned.
Regardless take the car in for an inspection; you don’t have to authorize any repairs.