Cough at 3months?

My little boy is 12 weeks old now and he has had a cough for the last week and a half. He had a 2 month checkup a few days after it started to get his vaccines and such, but the doctor never really addressed the cough. He is fine when he falls asleep, he will usually wake up once or twice coughing and then go back to sleep, and it’s not persistent, but he coughs infrequently throughout the day. My babysitter told me today he coughed so hard twice that he threw up. He hasn’t had a fever or been fatigued or grumpy or anything out of the norm other than some mild coughing. My question is, is there anything I can do to help stop it? And if I make yet another appointment with the doctor, is there anything that they can do for him?