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Statistically, this is most likely a bronchitis, and possibly an asthmatic bronchitis. However, if a chest x-ray has not been done, it would be appropriate to do so to exclude any underlying pneumonia.
If it is an asthmatic bronchitis, there are a couple of options for treatment. It would be reasonable to try a different antibiotic than the doxycycline, and the most commonly used antibiotic would be azithromycin. If the steroids were inhaled steroids, it would be appropriate to use systemic steroids, possibly with an injection followed by oral steroids. If oral steroids have already been tried, then there are some other inhalers that can be added, such as tiotropium. It also would be reasonable to use a long acting beta agonist, such as salmeterol.
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