I'm glad to hear from you!
As someone who has spent 9+ hours sitting in an ER waiting room in pain (serious but non life-threatening condition + major accident on the road that kept all the ER docs busy), I know that it's not a trivial thing to go in and have to wait, and I can understand why you want to avoid it and stay home. Unfortunately I think that you really do need to go. It sounds to me like you may already be in the beginning stages of DKA. Your ketones are variable, but you do have them at least sometimes, and that back and abdominal pain is worrying - it's a symptom, I had it when I was hospitalized for DKA years ago. It can mean that your kidneys are struggling.
The thing is, DKA can come on so fast. Especially when you're already weakened from a long and it sounds like nasty illness, and when you already feel so bad all the time anyway that you may not recognize the early signs. At first, it just feels like high BGs and the usual feeling awful that goes along with it - by the time it gets to a point where it feels distinctly different from regular high BGs, you may very quickly not be able to get help on your own, and you may not even realize that you're incapacitated. I was a kid at the time, and from the time my parents realized I was seriously ill and should go to the hospital, to the time it took us to get to the hospital (about an hour's drive as we lived in a remote area and didn't feel I needed an ambulance at the time we left), I became completely incoherent and incapacitated. I thought I had been conscious all the way to the hospital, but I don't remember half of the things my dad said I did or said in the car.
In any case, whether or not DKA is an issue, the fact is that you are an insulin-dependent diabetic who has a serious infection that has rendered you, for the moment, unable to control your blood sugar with insulin. That by itself means you need hospital care. Plus, your body is already unable to fight this infection on its own, hence the antibiotics and steroids. With such raging high BGs, it's even less capable of fighting off this infection, which in itself means BGs are likely to stay high (to say nothing of the effect of the steroids) so it becomes a vicious cycle that you may not be able to get out of on your own. Staying home and toughing it out is not likely to see you getting better any time soon.
Coming in as an insulin-dependent diabetic with uncontrollable high BGS and ketones should put you very high up the priority list as you have a potentially life-threatening condition at that point, so barring something like a major road accident that ties up A&E with people on death's door (god forbid), or gross incompetence (also god forbid) you should not have to wait very long once you go.