Welcome to HCM.
Dog bite if deep bites require longer time to heal. Every dog bite has to be washed thoroughly with soap and water within 6 hours and anti rabies vaccine
has to be taken. But if your dog has been vaccinated then a tetanus
shot will suffice.
I am suspecting bacterial infection of the bite wound as you are mentioning redness
and pain.Look for any ooze. If so, then I would suggest culture sensitivity testing of the discharge from the wound and then prescription of appropriate antibiotics based on the test results.
Over the counter painkillers can be taken for the soreness.
Rest the leg as much as possible.
Keep the wound clean.