how dangerous is it for my sugar to say over 600 on the meter?

It is INCREDIBLY DANGEROUS, ma'am.  Your doctor is doing exactly the right thing by "putting" you on insulin.

Without urgent, and immediate, treatment you COULD end up losing consciousness and needing to be admitted to hospital for emergency medical care.  I am NOT being melodramatic here, ma'am.  It really IS that serious.

Without emergency medical treatment, it's possible to lapse into a coma, and if recovery is not made, you COULD die.

It is dangerous ,., slowly dangerous.
Too much sugar in your blood makes it thicken and reduces circulation,
Your feet feel it first, because they are the furthest from the pump (heart). Feet start to go numb, injuries happen and you don't even feel it and since there is poor circulation to your feet, it is hard to clear up the infection.
This is why SO many diabetics end up having to have their feet amputated.

And that high blood sugar will slowly kill your eyesight ... and all your other internal organs, since it will hinder circulation and your organs will slowly fall apart.
Anything over 140 is dangerous, but the higher it is over 140, the more dangerous it is.