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snotty nose,deep seal bark cough,pulling@ear;Pediatrician gave her somethin4caugh&it wrkd4a wk but its back 9mths old

She’s had the cough for a while whatever the Pediatrician gave her helped & cleared what sounds like congestion for about a week or2 but now she’s got the green thick snotty nose and her cough sounds just as bad as before. How do I know if it a secondary infection or just something common? She been playing with her ear last 2days she’s 9mnths old and doesn’t have teeth yet I don’t wanna take her in unless I need to