There are too many questions regarding your question to give a succinct answer. Is the horse in training at this time? Did he bleed during a race, a workout, or some other event?
Most often, coughing and bleeding occur because of a lung infection. Most likely, your horse has some type of lung infection which predisposes it to bleeding. You need a veterinarian to examine the horse, especially with a fiber-optic endoscope to look down into the trachea and lung itself.
Other areas that could cause bleeding include a guttural pouch infection, exercise-induced pulmonary hemorrhage, or some other condition of the lung or respiratory tract.
As for medications to use, it must be determined what is causing the bleeding before prescribing any sort of treatment.
Also, many racing jurisdictions have very specific rules as to what medications can be used. Again, an equine veterinarian, especially one with racetrack experience, would be the best choice to advise you.
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