1920s East Coast Home

I’ve been having plumbing issues lately. I have a floor drain directly beside my main sewer line in the basement. It shoots up like a geyser when I flush the toilet but goes back down. It overflows when the shower is used, and the water that’s supposed to be in there rises during rainy weather. I had the main line snaked and the plumber got 20 ft in (from the basement) and hit metal. He said call the sewer authority. They looked and said everything was good on their end. I’m at a loss.