Refund the fee for the free plan

I signed up for a one-month free redemption code and tried to cancel after using it for a month. But they blocked my cancellation, telling me to update my payment information. They even blocked the plan I was already using. Out of frustration, I updated my plan, and they charged me a fee. I canceled, and they charged me another fee? Is that right? There's a limit to asking for a refund.