My DD (6) sometimes has a blueish tinge round her mouth. Not her actual lips but just around the mouth area.
She has suffered from bad, persistent coughs in the past and I've twice had her at hospital when she became very wheezy during particularly bad colds. This time, she is getting over a cold but still has a really bad cough (no wheeze though). She's not (so far) been diagnosed as asthmatic though has received an inhaler to get her through the worst of it.
Though she seems a lot better and has been diving around, the cough is still there and sometimes she sounds breathless. I have an appointment at the doc's on Monday and don't want to be fobbed off.