When it comes to a persistent dry cough like yours, Ayurveda can indeed offer some relief not just for the symptoms, but also for the underlying imbalance. The herbs you mentioned—Vasaka (Adhatoda vasica), Tulsi (Ocimum sanctum), and Mulethi (Licorice)—are all effective options. They each have unique properties that help soothe the throat, reduce coughing, and heal the respiratory tract.
Vasaka is known for its expectorant properties, helping to clear the airways; you could use it in powder form—mix half a teaspoon with honey and take it twice a day. Tulsi is a powerful herb that helps boost immunity and is often consumed as a tea, maybe add a bit of ginger for an extra kick. Mulethi works wonders for soothing a sore throat and can be chewed directly or taken as a decoction.
Now, about your living environment, dry air can definitely exacerbate a dry cough. If possible, consider using a humidifier, especially at night, to maintain moisture in the air. Ayurveda also suggests Nasya therapy—applying a drop or two of warm sesame oil or ghee in the nostrils —this can support nasal passages hydration.
Diet’s impact can’t be overlooked either. Avoiding spicy, oily, or very dry foods is indeed advisable. Try to incorporate warm, moist, easily digestible foods. A warm soup or stew with ginger and turmeric can be soothing.
As for how long it might take, Ayurvedic treatments tend to offer steady progress. Don’t expect overnight miracles, but with consistent use, some improvement is usually noticed within a week or two. This isn’t fast like modern meds, but it aims for a deeper, more sustainable relief. However, if your cough is persistent, never hesitate to consult with a professional practitioner - getting an evaluation can be key to finding a truly lasting solution. Remember, each body is different, and what works for one person may need adjustment for another.