Best medicine to cure dry cough, wheeze and sometimes short breath that last 2 months already?

This is difficult to determine without a review of history/exam and likely testing. Potential causes are many and treatment would vary with the cause. If it has gone on that long, it needs an in-person evaluation.

Any cough lasting longer than two weeks needs an evaluation by a pulmonary specialist. This is especially important in an area where tuberculosis may be endemic. Wish you good health!