Skin around my 3 month olds mouth, bluish/purplish?

This isn't all the time it's just a few times during the day the skin around his mouth is kind of a blue/purplish color. He's had a cough for almost 2 weeks and been congested, we went to the doctor on Wednesday and she said he sounded real "junky" but said it was just a lot of snot and that's what's making him cough. Which it sounds like a flemy cough. Anyway, I would've asked her about the skin color but I just noticed this a Thursday. He's been fussy during the day but I think he's teething bc he's drooling and chewing on his hands a lot, and then his nose being stuffed up makes him mad, too. But there will be some times when I'm holding him or he's in his swing he just gets really mad and cries a cry like he's hurt or scared and stiffens up his body and kind of arches his back. He does fine when he eats and everything, there are no problems there and he burps great most of the time. No fevers. No wheezing. Sound just like a normal cold and teething problem? Any advice would be greatly appreciated. Thanks in advance.