Constant cough and irritated throat

I've been coughing non stop since September, the doctor told me to take an inhaler which is okay but doesn't help most of the time. The cough started honestly out of thin air and so I was off school for 2 weeks. Now it's December and it's going bad again and well the cough is always there and my throat is always irritated or full of mucus. It's not allergies but it's annoying the hell out of me