PSN Account on PS3 and PS4

I have a PS3 and PS4 and when I got my ps4 I created a new PSN account without thinking about it...a silly decision that now haunts me as I'm finding the issue extremely difficult to fix. For one, it took a long time and a lot of PlayStation Network "experts" to help me figure out how to sign into the same account on both playstations because I kept getting the "you cannot sign in using another user's sign in ID" error when I would try on either one. This was fixed by creating a new user on my PS4... The problem now is that I would prefer to use the PSN account that I made on my PS4, not the one on my PS3, and I can't figure out how to get it to let me sign in with it on the PS3. Is this just not possible?
Thank you for the help, I am a little more than frustrated!