If your child runs out of eg. cough syrup, your house has got an exactly the same medicine prescribed to your child previously, but this is prescribed to an adult but unopened, would you feed it to your child? At the dosage stated for your child @3.5ml.

If it is the exact same medication, I think it is alright. However, if it is a cough and the child has not recovered after finished the prescribed medication, I would go back to the doctor as it seemed like the medication is not working. Would want to try another medication instead if there is no signs of recovery.