If you've got it on your phone then you've still got the information so no problems there.
It can't be wrong if it works on the phone.
When you tried to reinstall it did it tell you it was the wrong password or did it tell you something like it can't verify it?
Because it's common to say it can't verify and refuse to do it and you just have to come out and then usually it works. It's been like that on every email client I've ever used Windows and Mac. It's a real pain but it happens all the time.
It's best to do it in 'mail>preferences>accounts' in my experience rather than just straight to the the Accounts page
Furthermore, make sure you've entered all the info correctly as it's really easy to enter smpt rather than smtp and a good password can be easy to get wrong especially if you accidentally add a space before you start.
And finally you could use the cloud. Back up the phone to icloud making sure you include all your accounts then sign in on the mac and it should do it automatically for you.
But persist. It can't be wrong if you can get in on the phone so it's something else that's the problem.
