You can't delete an account, and all of the account's downloads will remain tied to the account.
On your computer's iTunes you should be able to edit your payment info by going into the Store > View Account menu option and logging into your account, and on your account's details page there should be a payment link. If you are doing it on your phone then tap on your id in Settings > iTunes & App Store and tap on 'View Apple ID' on the popup and log into your account - that should also give you a payments link on your account's page.
Changing payment info : http://support.apple.com/kb/HT1918
If you haven't already done so then you may want to contact iTunes Support to let them know : http://www.apple.com/support/itunes/contact/ - click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption