Replacing "guts" of a toilet

Hey,

I had some water issues a few months back that shot sediment into all of the pipes in my house, which blocked all of the water from flowing into all areas of the pipe. I drained and cleaned all of the pipes out and the water works better then ever. This is except the toilets in my house. I believe the sediment got into the "guts" (for the lack of a better term) of the toilet and needs to be replaced.

Being a new home owner, I was not sure how involved this project would be or should I call on a professional? I am looking for any and all suggestions on how to fix this without buying anything. Thanks everone.

Nick