Thank you for your query.
How long has your daughter been having the antibiotic and which one? How is the infection in the nail area? As you have not provided the information I believe she must be improving.
The red spots on the chin area are unlikelly to be related to the nail infection
or to the antibiotic being used. I suggest you apply some mositurizing cream and observe.
I hope I have answered your query to your satisfaction.
Wishing your daughter an early recovery.
Rajiv K Khandelwal