What is the cause of pus 3 days post nose filler and what does this mean? (Photos)

Please seek the advice and help of your injecting practitioner immediately! You need to be seen by them and referred on if they cannot manage this current presentation. The pictures represent what could be a vascular occlusion or injection and you need medical management for this 

This could be a viral infection if you have a personal history of fever blisters on your nose. Whenever somebody develops an infection, it tends to declare itself roughly 3 to 5 days after a procedure. Since infections in the mid face can cause retrograde spread of infection to the brain, this should be evaluated promptly by your doctor, or another facial plastic surgeon. I wish you well moving forward with this. Sincerely, Dr. Joseph

This is a risk of injecting fillers to the nose, where the blood vessels either get compressed OR the vessels get filled with filler and cause blockage to the skin which causes this.  You need to get to your doctor immediately for treatment.  Best, Dr. Emer.