Hi Suz,
I am sorry you are in my world of control right now. It isn't pretty, but you need to learn how to deal with it.
First off, I am sure you know how good, but how bad prednisone is for your body. It fixes things fast, but damages you organs fast too! You need to get off of it as soon as you can!
The highs can be quite high @ 500s and up, 600s are pretty common too. Most meters top out at 600, as the chemistry used, does not have the range to be accurate above that, so you get the HI code.
It will scare you at first at how much insulin it takes to get your bgs down, but it is vital to get you bgs at a decent level, lets say 250 or less. Eating will always be a problem and much more insulin will need to be taken, as to how much, there is no formula, so you need to keep testing, to get it down as quickly as possible.
As stated before, you can set up a sick day basal profile in your pump. You will need to experiment to see how much you need to keep bgs down, when on prednisone. Basals may need to be much higher than you feel comfortable with, but having high bgs for a long time, will absolutely start causing bad things to go on in your body. Therefore it is vital to get your bgs down to acceptable levels. It is no fun and it is scary, but again, you need to do what you need to do, to get you bgs right!

We are here to help you get through this glitch, so ask about your concerns and we can tell you how we have overcome steroid use. I am sure our long term friends will add their help also, just know, you can not have prolonged high blood sugar. It can get ugly!

I hope this asthma issue concludes for you soon. I further know the bronchial issues will go away at the same time. This is nothing to play with and I am sure you know, it can lead to pneumonia, if left untreated. You should be on the phone with your doctor, if you feel any worsening of symptoms.
prayers and good Karma are being sent you way!
Itsme Wayne