ive got the allmost the same problem, but i did receive an email on my rs account that the transaction has failed, but the money is booked over to jagex so i dont get it where it did go wrong...
Exploring Ironman mode
Have you received an email confirming the purchase?
If you have, check it to see that the right account is mentioned.
You should also see a message inside the 'Messages' tab in account management.
Can you see a message in there?
If there is no message in your Messages tab, check that the email has mentioned the correct account as the membership may have gone to another account.
If there is no email or message on your account, it means the purchase failed.
Check your credit card statement again. Is the payment still showing?
Also, your posting account (BlackerCrown) is showing that it has a membership.
Is BlackerCrown the name of your account in-game?