For a two-month-old baby, dosages of medications like cefpodoxime (an antibiotic) must be calculated precisely by a doctor based on the baby's weight, not just age. Additionally, antibiotics are used to treat bacterial infections and are not effective against viral dry coughs. Giving incorrect dosages to an infant can be harmful. Please do not self-medicate your baby. I highly recommend consulting a pediatrician so they can safely evaluate your baby's cough, determine the underlying cause, check their exact weight, and prescribe the correct treatment.