1999 Toyota Corolla Loose Drive Plate/Flex Plate

My car recently had a spark plug wire failure which resulted in the engine vibrating excessively. Once I replaced the spark plug wire, the engine runs fine, but I believe the engine vibration caused by the failed wire has loosened the drive plate/flex plate on my car.

At idle when in any gear besides park and when accelerating from a stop, there is rattling noise that comes from the rear of the engine, towards the driver's side on the left. The noise disappears once the car is up to any speed over 20 mph and runs fine.

Is my suspicion correct? Would a loose drive/flex plate be to blame? If so, how much would it cost to be repaired assuming no new drive/flex plate is required? How much if a new plate is required?

Also, is there any way for me to check and tighten the flex plate myself without removing the transmission?

Thank you very much!