How can you tell the difference between an allergy and a cold? (Please read details)?

My daughter has had an on and off cough since the beginning of the school year. The first cough and runny nose lasted for almost 4 weeks. The doctor told her to ride it out, it was just a cold.

Two weeks later it came back, this time with a headache and fever. Her doctor gave her Amoxicillin. (strep throat)

She was finally better until this past Wednesday when she developed a terrible cough and runny nose again. She felt better by Friday, but now it is Sunday evening and she can’t sleep because she is coughing. My husband is now convinced she has an allergy.

I will call the doctor tomorrow, but I was hoping to hear from someone that can possibly put my mind at ease so I can go to bed and not worry all night.