Do I need to go to the doctor?

I have a cold...sort of. It's really just a cough and a little congestion. It started out worse but is just a nuisance right now and a very minor one at that.

Here's the thing. My cough hasn't been very productive, and there is clearly mucus down in my chest. Actually right now, I can hear it and feel the roughness when I breathe deeply. Like, if I open my mouth and breathe deeply, there is an audible whistle coming from my throat.

Is this something I need to be concerned about (since my cough isn't bringing it up and out)? I've never had a cough quite like this. It is better than it was (less frequent), but I'm worried that the gunk is sitting there in my chest.

I got this cold from DS1... He has had the cough (but his is/was very wet) since the beginning of the month. We took him to the pedi since the cough lasted more than 3 weeks, and she said he's fine, just has a lot of gunk in his sinuses. His breathing sounded fine. (As an aside, at about 2.5 weeks in, I could also hear it when he would breathe through his mouth. I called then, and they weren't concerned since he didn't have a fever.)