My iPhone 4s Apple ID Password Won't accept after I changed the password, what can I do to fix this?

I had forgotten my computers password and had to do a systems reboot on my Macbook Air to set up a new password. When I did, I had to reset all of my passwords into my computer and then on my email's and iCloud because I had forgotten all of those passwords also (in hindsight, resetting passwords at two in the morning was a very bad idea). I have been trying to figure out what I did wrong with my phone and nothing seems to work. Following the instructions to resetting the network stuff but that didn't work. I can't reset the phone itself because of an app that needs to be turned off, which it needs the password to use and puts me at square one. I almost feel that the only way I can fix this is to just get a new iPhone altogether! Does anybody have an answer for this?