Setup Two Account Admin Permission

We bought a new laptop yesterday. Until now we both had our own. So we both have our own stuff we want to move there. We set up two accounts, both with admistrator permissions. But we would like those accounts to not "work" together. Like for example, we don't want our pictures, music etc to be seen from the other ones account. But now it does. We both want to put them to the D drive and only see our own stuff. Because it gets really confusing with the amount of stuff we have. So when I go somewhere, I only want to see the things I have put there, not his things. How do we do this? Also I noticed that if he or I remove something from the desktop, it goes away from the other account as well. That is really not something I want. I want the accounts to sort of work like two different computers.