Hello thanks for the query
It takes about 2-3 days for an antibiotic to start its effects. So don't worry and wait for the positive response otherwise consult your doctor to revise the treatment. Follow some instructions that helps her to recover soon: Firstly give her steam inhalation and nebulization and try to expel out the phlegm as much as she can.
Try to protect your child from changing climate and wet cloths.
Don't allow her to drink cold water, cold drinks, fried or oily food and chocolates.
Keep him in Hygienic environment
The cause for frequent cold
may be Tonsillitis
, Unhygienic environment, Respiratory Track diseases etc.
Consult your doctor and rule out the cause and follow the instructions.