I always bring my baby to paediatrician at Baby Bear Children'S Clinic 849 Woodlands St 82 #01-209 Opp Woodlands North Plaza, 730849, Singapore p: 62696928 f: 62696929. but I'm not sure how much they charge for coughing, so far I always go there for immunization.
I ever took my son to 888 Plaza Family Clinic (Dr Loh) for having flu at that time he was 2weeks old. He charged me less than $60 & gave 1 bottle of medicine. Well, it worked for my baby. Dr Loh has been our family GP for quite long time, he has many patients & very friendly. You can try to call the clinic first to check about the charge. The phone no is 6368 8762