Cold and cough in 4 month baby.

Respected doctors . I have two sons One is 4 years old and other is 4 month old. My older son has cough for last month . It is wet in nature. Actually he has pneumonia since 1st birthday. Each year 2 -3 times he suffered. On chest  xray report pneumonia is confirmed  and today doctor prescribed medicine. He has no fever at all but wet cough only. And Now my 4 months son has been suffering from cold cough sticky eyes throat nose and chest congestion for last 10 days. But from past 3 days he coughed a lot at late night about 3-4 am. And after waking up at 8-9 am. And coughing is very painful for him. Only that time mucus can be felt from nose to chest but unable to remove. Neither through sneezing not through vomit. He also not having any fever Can he also get pneumonia. Is it possible.