Do I have asthma again?

Patient: I had a cough for about 3 months starting in november, so I quit smoking but it hasn’t gone away. I’ve been off cigarettes for over 2 months now. People keep saying that it’s my lungs clearing out, but for this long? It’s kind of like a tickly dry cough,coughing doesn’t seem to help. It always happens in the morning, then it will clear up. But I will have to clear my throat through out the day. If I eat something cold, or even just go out in cold weather, the dry cough comes back. My breathing doesn’t feel right since November, it feels like I have to take a long deep breathe. I had asthma when I was a child, but I grew out of it. Could I be getting asthma again?