Lingering cough after cold going on 6 weeks

I’m 28F 5’0” 130lbs no smoking, currently taking Noscapine for my cough, otherwise no medications. I had a cold about 6 weeks ago. I had a fever that at its highest was 38.5°C and then I spent a few days at 37.7°C. The fever would come down with paracetamol but I'd have to take it every 6 hours or so or it spiked again. Fatigue, body aches, and a dry cough. I tested for Covid and it was negative. I let it run its course and only took Paracetamol and Noscapine.

A little over a week later, I was feverless but I had a persistent cough. Then I developed white spots on my tonsils and it felt like my throat was closing in. I saw a doctor and they prescribed 5 days of antibiotics for tonsilitis. The spots have since gone away but the cough is still present and although it feels dry, I sometimes cough up a little bit of phlegm. Cough medicine does not seem to be helping. I am still tired and can get a little bit out of breath after walking a distance. Should I be worried that I still have this cough after 6 weeks? My throat has started feeling a little bit scratchy again but besides that and this lingering cough, I have no other symptoms.