I would like to create a trigger that creates a record. I have created a wizard where an outside user creates a record. I would like a trigger to run when the user saves the record they created through the wizard. I would like the trigger to search a different objects records for similar email adresses. After doing that if no similar addresses are found I want the trigger to create a new record. Here is what I have so far.  Here is the error that I get:

Apex trigger ReferralTrigger caused an unexpected exception, contact your administrator: ReferralTrigger: execution of AfterUpdate caused by: System.FinalException: Record is read-only: Trigger.ReferralTrigger: line 22, column 17

trigger ReferralTrigger on Referral__c (after insert, after update) {
    
    List<Referee__c> Ree = [SELECT Referee_Email__c, Name, Id FROM Referee__c];
    Referee__c newRee = new Referee__c();
    Boolean add = false;
    
        for(Referral__c Rf : trigger.new){
            for(Referee__c Re : Ree){
                if(Rf.Your_Email__c != Re.Referee_Email__c || Re == null) add = true;
            }
        }
        if(add == true){
            for(Referral__c Ref : trigger.new){
                newRee.Name = Ref.Your_Name__c;
                newRee.Referee_Email__c = Ref.Your_Email__c;
                newRee.Referee_Phone__c = Ref.Your_Cell_Phone__c;
                newRee.Referee_City__c = Ref.Your_City__c;
                newRee.Referee_State__c = Ref.Your_State__c;
        
                insert newRee;
            
                Ref.Referee__c = newRee.Id; 
            }
        }
}