Cat bite - Advice Please (A bit gross)

[Underwhelmed]

My cat bit one of my fingers last weekend when I tried to remove her from a stand-off with my other cat. (She's never bit before).  I went to an urgent clinic on Tuesday after it showed signs of infection (swelling and redness) and was prescribed antibiotics and had a tetanus shot. It's been about 30 hours since the first dose and the finger has swollen further at the site of the bite. I'm assuming it's going to burst at some stage so is it better to go back to the clinic for them to drain the site or let it occur naturally? And how long long does it take the antibiotics to work?
thanks