What could cause a persistent cough with foamy mucus?

Thank you for your question. From the clinical history that you provided, I agree with the doctor whom you saw and with Dr Winston Lee that your symptoms are suggestive of acid reflux from the stomach. Specifically, since your symptoms are mostly in the throat, it is called Laryngopharyngeal Reflux (LPR). The most likely reason that you have a feeling of something stuck in the throat or a feeling of a “lump” in the throat (aka as globus sensation) is due to swelling of the voicebox (larynx).

Thank you for your question. Cough is a reflex meant to protect your airway from an irritant (e. g. mucous, foreign bodies or virus/bacteria). When persistent, it is usually a symptom of a condition. A cough lasting longer than 8 weeks is called chronic cough. Common causes of chronic cough in children include problems arising from the nose and sinuses (e. g. allergic rhinitis, sinusitis), lungs (e. g. asthma, bronchitis, foreign bodies) or stomach (acid reflux).