Persistent cough in 10 year old

My 10 year old DSS has had a cough for over a week now and stayed home from school the last 3 days of school last week. He's still coughing over the weekend (which assures us he's not faking it at all). One morning he was coughing enough that he even vomited. Luckily that's only happened once.

DH has been giving him some cough medicine, but I'm not even sure if that's the right thing to do anymore with medical recommendations often saying not to use cough medicine. We currently have him in his bedroom with a humidifier going.

I keep reading that you should see your doctor if a child has a cough for over 3 weeks. It's only been a week so far, so we haven't taken him.

Does anyone have any suggestions as to what to do? We don't even know if we should keep him home from school tomorrow or not. I know most contagions would be gone by now, so I doubt he's contagious (also, no one else in the house has any symptoms), and he's missing quite a bit of school.

My doctor told me that it's normal for a cough to last up to 2 weeks.
What kind of cough is it? Dry, phlemy, etc.
Any other symptoms?
If he's congested you could try vicks or something similar?
Hot (not too hot obviously, just enough to get the room a bit steamy) shower or bath?
For DS (12 months old) I put some vicks on a hanky near his cot which seems to help when he's got a cold.

Hope he's feeling better soon.