I sympathise, Arthur, and wish you a full recovery with pain relief as soon as possible.
As I explained to Slip in a previous thread, the usual way to cure a dental abscess is by the dentist or dental surgeon cutting into it to drain away the pus ( fluid containing the bacteria / bugs ). Indeed, antibiotics may not always be needed for dental abscesses unless there are complications ( like local spread ). If they were needed, amoxicillin ( a type of penicillin ), as prescribed in your case, is appropriate.
Hopefully the antibiotics will “ kick in “, as you say, but presumably this is prior to your dentist / dental surgeon draining the abscess.
Get well soon!