Contact your CC Company and explain the situation to them.
A block can be put on the account so that no more payments can be taken from you by this Company. The CC recovery team might also be able to recover your money for you if the charges were not justified.You should also have new cards issued for your account. This will only take a few days to sort out and you will not need to change your passwords.
Just remember to inform anyone who might receive payment from your card for a service on a regular basis.
Hope it all works out for you.