You have to log out of your paramount plus account to log into the new one. I currently have paramount plus through walmart+ and it works fine, but unfortunately I don't think you can upgrade to premium. The walmart+ app says you can only get paramount plus with ads. Whenever I try to get into my account through paramount plus, it says: you subscribed through walmart+ please use your walmart+ account to make any changes. The problem is inside your walmart+ account you can't make changes to paramount plus, all you can do is get into the paramount plus app. So as far as I can tell you can't upgrade it.
The number to Paramount plus customer service is 1-888-274-5343
Walmart + customer service is 1(800)323-3897