cough with phlegm can be a very sticky issue. my daughter had this problem which lasted 6 months. she's seen a doctor which gave her 2 courses of antibiotic with other medicines which didn't work.
after that, my daughter seen a doctor at hougang (block 683) and recovered after 2 visits. she was given inhaler (2x/day) which was easy to use, neulin for her phlegm, dasedyl for her cough and prednisolone for anti-inflammatory.
as for food, avoid cooling drink (even if they are warm) like chrysanthemum, ling yang and barley. avoid melon group of fruits like water melon, honey dew, winter melon, rock melon, cucumber and etc. of cos, avoid cold drinks and ice creams!
warm honey is good.