Welcome to healthcare magic
According to the description you seem to have fixed drug eruption
Even after the rash subsides the post inflammatory pigmentation
is notorious to stay for months to years.
Do not take augmentin or even penicillin group of drugs in the future as the rash can occur over the same site again.
You may apply a cream containing hydroquinone
2 % and or kojic acid twice a day for the rash to lighten faster. Get it prescribed by your dermatologist
Hope this helped