Can anyone tell me more about Moxarella Catarrhalis infections? How serious are they?

Sex: Female Age: 27 Weight: 49kg Height: 5ft 2"

I had pneumonia in March, caused by two infections, a Moxarella infection and another bacteria my GP's paramedic described as a "flu thing". I started to get better after some Doxycycline, but 6 weeks later I've gone back downhill. I'm coughing every 5 seconds again, and it's a very violent cough. They've sent off another sputum sample to see if I still have the same infections, and have said my immune system is likely not coping too well. But I couldn't get any answers on what this infection means for me. Is it typically easily treated? Just it just need a longer course? Or should I be asking for something different? Thanks!