Hi Sammi, and welcome 🙂
I had ketoacidosis when I was diagnosed, and I was sent straight to hospital and kept in for several days until they'd got rid of the ketones. I'm very surprised that they've sent you home while you've still got ketones and your readings are still so high - my initial reading was 20 and it didn't ever go much higher. Don't want to worry you, but tbh I'd be going to A&E if my readings were going into the 30s and not going down below 16. If you didn't already have an appointment on Tuesday I'd suggest you get yourself back to hospital asap. As you have an appointment for Tuesday it's probably OK until then - but if you start to feel any worse, please don't wait until Tuesday, do go to A&E straight away.
I'm also surprised they've put you on mixed insulin - it's a very old-fashioned way of treating type 1. When you go in on Tuesday, ask them about MDI (multiple daily injections). You have to do more injections, but it's much more flexible than mixed insulin, you can inject for what you want to eat rather than eating for what you've injected - and if your blood sugar is too high, you can do a correction dose to bring it down. I can't think of any reason they wouldn't put you onto MDI, at least now you've got used to injecting.
Good luck, and please let us know how you get on. And if you have any more questions, please don't hesitate to ask - someone here is sure to be able to help.