Remedy for my 3 year old daughter

Hello Sir, I am seeking a remedy for my 3 year old daughter Urja. Following are the details to help you diagnose the problem:

General Details:
Urja was born 7 year after my marriage through an IVF treatment. I had been diagnosed with PCO problem. She was born with a health weight of 3.18 Kg. She had jaundice soon after her birth but was under control.

Her Physique details:
Urja is a tall and broad girl with good hair. Her skin is extremely dry.

Her eating Habits:
Urja has a good diet. She is a vegetarian. She loves chocolates and ice creams. She like eating tomatoes in salad.

Problem:
I have quite a few problems with her.
1. She has chronic cough which increases at night. Generally, 2-3 hours after she has slept. She than vomits, which consists of mucus with sme food she had at night. After vomitting she is able to sleep again with some coughing. She generallies vomits at least once in every 3-4 days. Rarely, it happens that she doesn't vommit for 15 continuous days. However, never more than 15 days. Vomitting has always happened during evening/night time. I give her Balladona 30 for cough. She has generally dry cough. Morning she has lots of mucus coming from nose. Once or twice in a month she gets cold as well.

2. She has a sleeping problem. She doesn't take any afternoon nap for the past 1 year. Evening she sleep, but she oftens speak while sleeping. Generally she speaks of things happened during day. She never had a continuous night sleep. She always get up at least once during the night. Although she might sleep again 2-3 minutes after she has got up. Once in every 15 days she will get and cry a little bit (5-10 mins) before going to sleep again.

3. She has a fobia/fear to anything new. She is not a social child. However she has a fobia to go anywhere whether it is a party or anyones house. She is not comfortable with lots of kids or when she is in party. She starts crying if anyone comes to our house or if we go anywhere. She has started her Nursery school 3 months back but still has a fear of going to school. She tries not to sleep at night because of the fear of going to school next day. Let me know if there is a remedy for this as well in Homeppathy.

Thanks
Mansi