You can try repairing the problems in your User's folder or you can move your data over via the Shared folder to the new User.
Let's try a quick fix first...
Quit Mail
Go to User's Library
Scroll down to Containers - delete the com.apple.mail folder.
Scroll down to Mail - Rename Mail to MailXXX
Scroll down to Preferences - delete the com.apple.systempreferences.plist (you will have to reset items in System Preferences)
Log out under the Apple in the Menu bar.
Delete the Trash
Open Mail
Try adding your Gmail account.
Let me know what happens.
If you do decide to move to a new User...
This duplicates data so depending on how much free space you have you will need to be careful that you move then delete & empty the trash so you don't run out of room.
If you have an external drive, I suggest you clone your current drive as a backup in addition to Time Machine backup first.
Create a Clone backup:
A clone is an exact bootable copy of your internal drive. Unlike standard copying of all files to another drive, the clone software copies hidden files along with other in-use files that are not available when you copy over files to another drive.
Software used to Clone:
SuperDuper! http://www.shirt-pocket.com/
CCC http://www.bombich.com/download.html