You are absolutely right.
You are having scarlet fever.
It is streptococcal infection
It follows after throat infection
There is no itching, amoxycillin induced rash is associated with itching.
So, it seems that it is not drug reaction.
Antibiotics should be taken for about 2 weeks.
Apply calamine lotion for soothing effects.
It should not be left untreated, as it may lead to comlications ..ear infection, renal infection, pneumonia,rheumatic fever
You must consult physician and dermatologist
for perfect treatment.
Dr. Ilyas Patel MD