Go see an ENT soon as its just a young baby , it is good idea to seek help online but at first go and see the best ENT in your area and trust your doctors.!
I read your post , and my 2 month old is doing the same thing sometimes. Did you get any other answers for this ?
Are you sure it is saliva? Or can it be regurgitated fluid from stomach? Hope you let her sleep head end raised than the rest of the body.
An ENT specialist may be able to comment better. Sometimes a laryngoscopy may be required for expert opinion.
Hope this helps.
Best,
Dr.Thomas Antony