If you receive the error when adding your referees "Your hiring manager has blocked the use of personal email addresses from @hotmail or @gmail etc for Professional References." this means the company requesting your references has set a block on certain types of personal email addresses being added. Please try to find the referees official work / company email for the reference and add them using this.
You may also be able to contact the company and add the current HR Manager as a referee, who should be able to provide a reference for you.
If you are unable to find a work email address for them, or if they use a gmail etc as their official work email, please contact the company who has requested your references (your hiring manager) as they may be able to add this referee email for you, or provide advice on your next steps.