What Is The Treatment For Cough And Asthma In A Child?

hi my son is 10 in febuary, as a baby he sufford with croop and was in and out of hospital,a couple of years ago the doctor diagnosed him with a slight bit of astma and gave him an easi-breathe inhaler called salamol,only time this effects my sons health is when the weather changes,as your aware we have got bad snow and this as effected my son,on monday my son started with a cough and for the past three days he asnt eaten much but hes been drinking plenty of fluids and all he seems to be doing is constant coughting until he is sick witch i only think he his bringing flem up,he says he feels a bit weak witch i can tell but he is still able to play with his things,he asnt got a tempreture its 36.5,he looks pale and says his throat hurts and sometimes his head and as had odd bit of nose bleed witch he does have regular without being ill this is probably from the pressure of coughthing,i rang my local doctor yesturday and i asked them for (amoxocillin) antibiotics on prescription witch there gave me now this normaly always works,i have been giving him antibiotics 3 times a day also calpol since yesturday and putting him karvol on at night and in the mean time he uses his inhaler,do you think i should carry on the way iam doing and she what he his like in couple of days then it gives the antibiotic time to work or do you think its best to get him checked?,its just that i have a 10 month old daughter and i wouldnt like her to get it please can you advice me what to do thanks nick.