What can I do for a cough?

For a couple weeks my son has been coughing. At first I thought he had a cold so I gave him medicine it still didn’t go away so I thought maybe allergies so I gave him medicine and it didn’t help. As I’ve been watching this cough more I’ve noticed he is only does it when he’s active running around and playing. My neighbor mentioned that it could be asthma. I don’t really know much about it since I’ve never dealt with it. My question is does it sound like asthma or not? And if it could be what do they give a 2year old for it. I’ve already made an appointment for him this week, but I just wanted to asked and see if anyone had any advice. Thank you!