During a recent freeze our shower froze. Last week water came out of the faucet, but it took the water at least a full day before going down the drain. I plunged the drain and a dark colored rust came up. After a day of waiting the water finally went down. I poured Liquid Plumr down the drain, after about five hours it finally disappeared. I then poured hot water down the drain, and again waited. Again I plunged and more dark rust came up through the drain. Do I have a clogged drain or is a pipe broken.

When I plung the drain in the shower, rust comes up.