at night and early mornings is a suggestion of airways disease such as asthma in most children.
NO alterations in diet is recommended unless a specific food allergy
is proven. Cow's milk allergy
and cough is controversial and not proven, so please get allergy tests
(blood tests or skin tests) and get an allergy diagnosis before changing diet.
Reflux disease (acid in stomach) is also a possibility, and syrup omeprazole 20mg with or without domperidone
daily for 3-4 weeks trial is recommended.
At the same time, continue duolin inhaler and add singulair 4mg at night.
Nose bleeds to inhaler device suggest wrong technique of administration, so suggest get a spacer device to attach to end of inhaler (children must always be provided with a spacer device).
Allergy to house dust mite, cockroach etc are always important to exclude as avoidance of further exposure is key.
I hope that was useful.