I was told the best way....?

ok so i was told the best way to get your horse in shape for barrel racing is to lope it trot and walk it. walk it for a half mile then trot it for a half mile for a week then go up till you hit about 6 to eight miles but every time im done walking her for the half mile and then i trot her but shes coughing before the half mile is even done am i pushing her to hard or is she sick. p.s. shes a 9 year old Arabian mare previous brood mare has had 7 colts does that have anything to do with it