2 month old baby boogers

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My baby started having a runny boogers here and there 
After he got he's shots (which I did tell the doctor before the shots where given) went home he got a fever took him to the ER and got sent home with Tylenol he had fevers here and there for 3 day but it's been awhole week now he still has boogers a lot and now has a cough 
Does anyone have any advice on how I can cure his cough or his boogers