Should dog continue antibiotics?

Simba (cocker spaniel, 6) had his nail cut right back under sedation Monday 27th. Wednesday bandage came off and vet was happy with how it looked, nice and dry, but surprised it was still so sore so prescribed more painkillers.

By Friday he was limping and in a lot of pain with a tiny dot of pus and blood between the nail and the skin. I took him back to the vet who still thought it looked ok and prescribed three days of antibiotics just in case (I had to push for this) and refused to give him more painkillers.

Today (Sunday evening) it looks even more bloody and sore. His course of antibiotics will finish tomorrow morning. He seems a bit perkier today but still in pain.

Should I take him back to the vet tomorrow to extend the course of antibiotics? Should I be demanding more painkillers for him?

Note he has not licked it and it was kept clean and dry for the first two days until vet cleared him for short lead walks on Wednesday.