2006 Honda Civic Shaking at low speeds

Hello,

I just recently got a rotation and balance on my vehicle. I found out bad shocks had caused cupping in my rear tires. They moved my bad tires to the front and put my good tires in the rear.

I was wondering if the bad tires is the cause for fairly strong vibrations. Vibrations are most noticable at mph below 15-20. I am afraid because I also feel the vibration in my brake and gas pedals. Will continue use of bad tires in the front affect the integrity of the rest of my vehicle.

I already got the rear shocks changed out but im still saving for two new tires. Im afraid the bad tires will hurt my car. Any help would be greatly appreciated.