since i don't know what's wrong, i am going to assume the worst case and that your macbook will need to have the hdd and logicboard replaced. I would suggest making a new account that is admin enabled. that way there is no real reason for apple care to be in your home folder. Easy things to do are clear cache, history, cookies in browsers. Also deactivate itunes. best cheap solution if you cannot spend money on external storage is send as many files as you can that are priorities to you gmail account.
But quite honestly, you don't have anything to really worry about. apple care wants to wham bam thank you mam that machine in and out as fast as possible, not look for the possibility of your creditcard info. Plus if it is going to apple care, it is most likely some sort of hardware related issue.