How to manage a 3-year-old's repeated asthmatic cough?

Hello doctor,

My daughter is 3 years and seven months old. She is a healthy kid. After two and a half years, we observed that she repeatedly catches a cold and a cough. The cold lasts for more than two weeks, followed by a cough. Her under-eye becomes dark. She breathes with her mouth and keeps her mouth open all the time. She once coughed continuously, and we rushed her to the emergency room. She was admitted, and a nebulization with oxygen was given. Our family doctor said that it was rhinitis and that due to the persistent cold, she had developed an asthmatic cough. She had wheezing last winter. Currently, we use Asthalin, Budecort inhaler, and Montair LC Kid syrup. Her cold is allergic, but the allergy test was negative. Even a slight climate change affects her.

Please suggest a remedy.

Thank you doctor,

Are there any side effects for the Budecort inhaler and Montair LC Kid? How long should it be given? Also, is this an allergic disease? I live in a first-floor apartment, and my house is extra cold. The flooring becomes too cold in winter. Will this impact my child? Also, there are green algae on the outside walls. Are her health issues due to that? Because I read somewhere that mold is dangerous and can cause health issues. Do I need to change my home?

Thank you doctor,

The recent symptom is that her eyes are watering. Her right eye is flowing. We observe that her face is not normal, and her under-eye area is swollen. She is sneezing every morning two to three times. Right now, there is no cough or cold. What are these symptoms, and what to take for this? Are they suggestive of some major illness? As of now, there are no asthma symptoms. Last week, her calcium level was down. So, we started Calimax P syrup 5 ml twice daily. Today, she is complaining of stomach pain after taking the syrup. Please suggest a medicine for this overall case.