How long does it usually take for a lung infection to go? i've also just started a course of antibiotics

It depends: It all depends on what kind of lung infection you have. Something like pneumonia usually takes longer to recover from than bronchitis or a viral upper respiratory infection. If it is a bacterial infection and you just started antibiotics, i think you should start feeling better within 48-72 hours, although it may take 7-10 days for full recovery. (longer if something like pneumonia, up to 14).