email account compromised

I am fed up. I have an Apple ID with 2 email addresses. I only use these email addresses for one specific purpose (news group) so there is a very limited number of people who know it. For at least a year I have been getting other people's emails because their email address begins with the same five letters as mine and an absolute deluge of spam from the US. I like to check my emails by logging in on iCloud but now every time I do I am told that my account has been locked for security reasons and I have to go through the rigmarole of unlocking it, which suggests someone is trying to hack into it. I would like to delete the old Apple ID and associated email addresses and start again, but how can I set up a new Apple ID and new email address without using an email address that I don't want to use anymore because it is compromised?