Negotiate with your credit card company
Once you have all the data and a sense of better offers to be had, contact your credit card company and request them to reduce your interest rate. If you have a good credit score and if you have a history of making your payments on time, you can negotiate from a position of strength.
You can ask them to reduce the rate, tell them that other banks are offering cards at a lower rate, and that you are willing to close your account and get a new card, if needed. If you are facing financial hardship and struggling to pay your bills as a result, you can explain the extenuating circumstances that led to your current situation and request your credit card provider to reduce your interest rate.