Thanks for writing to health care magic.
Dipping the ears under water should not cause much problem unless the ear drum is perforated. So do not worry about that.
When ever a baby is having cough
monitor the following.
1. Breathing rate. This should not be above 50 per minute in this age group.
2. Chest indrawing
3. Nasal flaring
5. poor feeding
If your baby does not have any of the above and continues to be active do not worry.
Just monitor the kid.
Hope this helps.