I've had brake pads and rotors checked. Mechanic said they were fine. Grinding noise becoming louder. Mechanic said it could be brake dust. Will brake dust continue to get louder? How safe is this?
Brake dust tends to cause squealing (high-pitched) noise, not grinding. Grinding noises are usually a lower frequency sound when heard from inside the car, and that suggests two metal parts rubbing together rapidly.
If the sound occurs only when braking, logically, it is extremely likely to be the brake system components. The 2010 Civic comes with disc brakes front and rear, so a grinding noise is usually either the brake pads contacting the disc rotor (after they've worn down to the pad's backing plate, or the brake caliper contacting the rotor. A cursory look may not be enough and it is strongly advisable to remove the caliper and pads and properly inspect all components. If your mechanic can't find the noise and it is loud and increasing, it might be time to find another mechanic.
The contact point may be on the inner side of the rotor which won't be obvious if only the wheel is removed for a casual look.
One other possible cause of a loud grinding noise under braking is the body contacting the tyres. This is possible if the suspension has collapsed or been modified to lower the body and braking further compresses the suspension, bringing the wheel clearance below the necessary amount. Look for marks on the bodywork around the wheel well.
In the less likely category: If the hub bearings were dry or had failed you'd hear a constant grinding. Similarly for the CV joints.
I would seek a second opinion as loud grinding noises only get worse and generally mean a more expensive repair due to more costly parts requiring replacement.