I hope you are getting some sleep Jesse!
I can't tell you what to do because it is your decision entirely -- but I can tell you about my own experience with lung infections. I have asthma so if I get a cold/flu it gets down in my lungs, and I am prone to pneumonia if get that kind of infection. Earlier this year, I had bronchitis, asthma, pneumonia, a severe throat irritation, and a collapsed lung in the space of a month. I needed to cough to get it all moving out, but it burned and hurt to cough, and it was so painful to swallow that I could barely do it - the sore throat was worse than all the rest put together. I would sweat too, and my chest and ribs ached. The only thing that stopped the pain and burning was the antibiotics. The first one I took wasn't the right one so it took a couple of weeks for them to get it right so they could kick in, but I felt so much better when they did. I had some cough medicine that helped a little with the swallowing so I would take that, then the antibiotics. If you are in the hospital, could they do intravenous antibiotics for as long as you are there? You could change your mind when you feel well enough to go home. Just something to ask about.