Since its hot to touch with oozing etc- the wound is likely to be infected.
Its better you take him to ER.
If there is no fever
, its unlikely that blood infection has happened.
Whenever dressing is done for open wounds, it has to be done in a sterile manner. Else infection can happen. A visit to doctor will sort out the issue.
Doctor will examine his finger, see how bad the infection is and decide accordingly.
If infection is bad, he might need oral antibiotics
too along with a clean dressing.
Hope my answer helps you.
Wish your son a speedy recovery.