Hi, I had gone through your question and understand your concerns.
12 years age is mostly related to
menarche only.May be coincided with your antibiotic use.
Do not get panic, 12 is not precocious,by high fatty food these days will get early menarchae .
No need to visit a physician, wait for some days ad observe for cyclic character.
It is very common to have
irregular periods in the early age.
Gradually it will come down to normal.
There is no test which can diagnose that it ,as a start of
menstruation.
Check for HB levels .
You can continue the antibiotic till the infection controlled.It will not cause spotting.
May be she is anxious ,and unable to understand what is happening.
Give her moral support and give nutritious food.
Hope this will help you.
Thank you.