I'm really concerned about this cold and cough that keeps coming back, especially with breathing problems at night and in the early morning for the past three weeks. I saw a general physician and the medicine worked for a week, but the breathing issue starts up again as soon as I stop taking it. What should I do about this?

It sounds like you may have asthma or an allergic airway condition triggered by cold or night-time air. I recommend consulting a pulmonologist for a proper evaluation, including spirometry. Continuing appropriate long-term treatment, like inhalers, may help prevent recurrence.