Welcome to the community!
When you accessed your My Account using your phone, did you click on the Phone details tab?
You may need to Log in to actually change the voicemail password.
Alternatively have you tried to access My Account via a computer? You should be able to change the voicemail password via Services --> Mobile --> My Device (near bottom of page) --> Update Voicemail Password.
I'm not sure if it makes a difference, but do you have a post-paid or pre-paid plan?
Hope this helps