How can I get rid of pneumonia without having to go to the doctors to get antibiotics I am also allergic to penicillin?

Not possible. There is a chance your body might fight it off with only limited damage. But also chance you can die. It's not the 1800's so go get treated with antibiotics, if is indeed pneumonia! there are many non-penicillin choices.
See your Doctor. Pneumonia is potentially a life threatening infection. You need to see your physician immediately!
Don't be afraid... Of your penicillin allergy. Penicillin isn't going to be the best choice for treatment of what you have anyway. Do be afraid of your pneumonia and go see your doctor. People still die of pneumonia. Remember jim henson?
You can't. If you really have pneumonia, which is a serious infection, you have to be evaluated by a doctor and if the infection is bacterial be prescribed an appropriate antibiotic. There are several which can be used in a penicillin allergic patient. Pneumonia will not get better on its own.