Cronic cough in infant

So when my son was about 6 weeks he started with a cough and some chest congestion. After about a week my daughter who is 2 started I brought them both to the doctor and she said a cold. Well after 2 days my daughter was better but my son was not so the next week I went back in and saw the physician assitant and she said it was caused by his reflux and to make sure he got it in the morning and keep him up right for 20 minutes after each feeding. Did not help the next week we had our 2 month well child and the doctor (another one) said it could be either a cold or reflux and should clear up. At 3 months it was still going on went in and saw the first doctor we saw and she said it was most likely reflux and should get better with solids. Now the cough is always there but sometime it is worse then others and he has coughing fits that wake him at night. It does not matter if he is upright or flat on his back. He is almost 4 month and it has been 4 weeks since we went in and we go in just over a week for 4 month well child. I just feel that something else is wrong and I want him to be better. Everyone is always like "What is up with his breathing" He is so raspy and feel like he needs to cough something out. He is on prevacid for his reflux and it help keep him from spitting up so I do not know if he needs to spit it up. It started after he was on the prevacid for a couple weeks. Anyone else have this issue? The last dr also said he may have asthma but we have never heard him wheeze so she said she wanted to wait on that.