The frequent cold n cough could be due to low immunity, entry into school and constant exposure to new infections. This is  quite common in kids and will be under control once her immunity develops. As for eating spicy, u cannot force her.  As she grows up, her tolerance to spices will increase. There is no connection to allergy or immunity here. Keep introducing new foods and dishes at regular intervals as they tend to get bored with the same stuff. Also try n make it colorful n appealing to her. Do not forget to include fresh n dry fruits in her diet,  besides veggies n cereals of course