If your three-month-old baby has been coughing and sneezing more than usual at night and in the morning, it's best to avoid over-the-counter cold medications. Instead, try using a good nasal irrigation technique to help with congestion. Congestion can lead to mucus dripping down the throat and causing a persistent cough. You can find helpful tips on proper nasal irrigation in the provided document. If you have any more questions, feel free to ask.