Who can say how long it will take, just be sure to take the full course of antibiotics and if the infection doesn't clear up then go back to your Dr's.
I think it depends on how long you've been on antibiotics for. Have you had a swab or test done on the infected finger so they know what type of infection it is? It could be that you're on the wrong antibiotic too.... that's happened to me in the past. If you've been on antibiotics for 2 weeks then it's probably best to speak with your doc. I hope the infection clears up soon for you.