Does teething worsen a cough?

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DD is teething at the moment. One has poked through and I can see another 2 white lumps.

She's had a cough for about 5 weeks now which has usually meant her coughing like a smoker for about 5 minutes when she wakes in the morning but otherwise not too much. However, since she started teething about a week ago she is literally coughing all night. Is teething likely to have this effect on her, or might it be something else that the GP should look at?

Other symptoms are general grumpiness and a tendency to get frustrated with everthing. She seems OK, but every minute or two she tenses up and growls.

I think they just generally become run down whilst teething..ds2 seems to have constant colds atm..

Is the tension normal? One moment fine then next she throws her toy against the wall, balls her fist and growls. Then alright again for a little while. She's not like this all day, but quite a lot! Its not like her at all, but I can understand that teething pain might cause her to be like this. She's also pulling her hair at the back of her head and above her ears (I don't think she has an ear infection).