Talk to Pulmonologist / Lung on Dry Cough And Migraine

I’m facing weird loud coughs with phlegm, since 3 weeks, just started on antibiotics 2 days ago , - Linzyle (5 days) 1 time - Nedor - Otryl syrup

But last night, I coughed to the extent that I puked but, the pressure build up to puke caused an extreme pain at the back of my head and now I can feel it in my jaw too,

What happened ? My head feels heavy right now and I feel my ear are closed too..