Blood streaks in green colour phlegm.

I have very small blood streaks when I clear my throat in the mornings along with green colour phlegm from one week. It started with a sore throat after going outside in cold air and polluted area. Consulted ENT and he diagnosed granular pharyngitis and prescribed antibiotics, anti allergic and betadine gargil along with an antacid. But I am still getting blood streaks in green phlegm even though I am using antibiotics from the last 4 days.No Sore throat  , No fever , No weight loss , No smoking and alcohol drinking habit , No cough, had history of nose bleed once, No nasal congestion, No snoring habit. I attached blood streak pics of the last two day mornings. This blood streak episodes repeats every year for me particularly in winters and whenever I feel col. This is making me anxious about my health condition although I am feeling fine physically outside. For second opinion Do I need to consult a pulmonologist or a general physici9an?