Brief Answer:
Please get her evaluated by a pediatrician

Detailed Answer:
Hello

Thanks for asking on this platform

I do understand your concern.Cough,cold with noisy breathing without any fever can be due to some allergy.
Fever is usually common presentation in any kind of infection.
The irritability with noisy breathing can be due to the spasm of the airway or due to stuffy nose.
In case of spasm of airway there may be associated breathing difficulty like increased respiratory rate or chest retraction.
In this condition it would be better to get her clinically evaluated by a pediatrician to check whether the problem is in upper airway or in lower airway,as the management differ in both the conditions.
If the lower airway is not involved,giving anti allergic like cetrizine,chlorpheniramine with decongestant like phenylephrine and some nasal saline drop will help.
So I would suggest you to get her to a pediatrician for better management.

I shall be glad to help you out if you have any more queries.
Warm regards

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