Mail on my iPhone 4s iOS9.1 won't delete messages. They keep coming back.

I'm on a 4S iPhone – version iOS 9.1. Since doing a routine update about a month or so ago, my iPhone won't delete messages. I now have over 8,500 messages in my InBox. Every time I delete them, they just keep reappearing in my InBox. How do I get rid of them? Is it something to do with iCloud? I didn't have that set up until recently either.

Please give me step by step instructions if you know the answer to this. I know others having the same problem.