@Andyheath1984,
Antibiotics are used for chest infections when you coughing up "ack stuff". Doctors don't always give antibiotics because they try to allow the body to fight off the infection.
If you have a "productive" cough or are wheezing (high pitched whistle when you breath out).... or a number of other symptoms - then they may prescribe antibiotics as this is more likely a bacterial infection. If all the blood tests have come back normal then it is difficult to say. Antibiotics are for bacterial infections, not viral infections.
You are obviously very concerned, for you and your wee step-daughter right now, and it's hard to know what to do if the docs are telling you everything is fine. You don't feel fine and your anxiety is showing here in your posts.
If I were you, I would call the doctor again - you are worried and the more you worry, the worse you are going to feel. Viral infections can go on for a long time, especially in the "flu" season.
I am not a medical person at all. Please do get medical advice. Don't be concerned if the doc thinks you are being overly concerned or protective - this is your health and the little girls - that is their job and you are the patient. Give 'em a quick call.