With new iPhone 5S can't get Apps to update

I got a new iPhone (5S) and a short time after that I noticed I had apps that needed updating. I thought I had selected automatic updates for apps so I looked, I had. ??? So I went into the App Store, clicked on Update, saw the apps that needed to be updated. I clicked to update and it asked me for my password. Entered it and it said it was incorrect. Entered it again, maybe typo, incorrect again. I then noticed ... UGH! ... that it had my previous email address (from 7 years ago) for my ID. I thought I had gotten rid of this problem. Being required to use an email address for an ID I have come to feel is ridiculous. I had this problem with iTunes after we moved and it took several years before someone at Apple via the Genius Bar seemed to get it fixed.

Well, I went to the Apple Store and they said what I had to do was put in the password I used when I was using the previous email. Ridiculous, I don't keep a running record of passwords. They said I had to re-purchase the apps I had gotten with the old ID. Also ridiculous. Does anyone have any idea how to fix it, how to get rid of that old email address (where is it anyway). I have no trouble with iTunes; I use the so called Apple ID (email address) and PW I established several years ago after we moved with no problem. My iPad updates the apps automatically; since the new system on the iPad it has automatically updated, I don't even remember doing anything, it just without my involvement since the new iOS been updating my apps on the iPad.

How can I get rid of that old email address? I looked at the answers to another question on the Discussion Board but that looked like a different situation from what I have. My iTunes recognizes my Apple ID and PW (I buy music, etc. with no problem), and my iPad updates my apps, how can I get the iPhone to update my apps? How do I get this email address issue resolved?