Is this Sony ereader app running on the phone?
Try the Bluefire app instead, or maybe Aldiko.
Some apps have issues with registration, Bluefire generally seems pretty reliable.
Also, some apps or the Adobe DRM server have issues where there are special characters in the password;
if necessary change to a simpler password (yes; against all the rules of good passwords, but that's the Adobe DRM infrastructure for you)
When you say and am able to log in on chrome do you mean you are able to log on to the Adobe website on Chrome?