You can't delete a household specifically. Households only exist if there are members assigned to the household and then are deleted if all of the members are removed.
Are you the only person in the household? It sounds like there might be two member records for you. Go to the Search box in the top toolbar (not above the Clubber or Leader grid). Put in your last name. If there is more than one match, a selection box will come up. If there are two results for your name, that means there are two separate member records. Open both and decide which one you can delete. If both have unique data, the easiest thing to do is take a screen shot of one and update the other one. Then, delete the extra member record. At that point the duplicate household should be removed.
If additional help is needed, send an email to support and we'll work with you to get it cleaned up.