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I'm happy that you have asked me to assist you with your child and hope that you can benefit from my many years of helping parents like you.
Infants can easily catch a cold from siblings and other close contacts but unlike older children, don't clear their throats or swallow mucous but tend to choke a bit on it.
As long as she does not have fever and is eating and sleeping OK then you can simply wait and watch. To help her you may use a cool mist humidifier on her while sleeping as well as elevating the head of her bed or letting her sleep in her car seat will help the drainage and keep her from coughing as much. There are no medications to give her but you many put saline nose drops in her nostrils, followed by suctioning, if she seems to have a lot of mucous in her nostrils as at her age she will prefer to breathe through her nose rather than her mouth.
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