Need help with my oscilloscope
What I gather from your post is that you connected one of the leads of an auto transformer, wich is not isolated, to the oscilloscope ground. The fact that the probe was in x10 mode or even the voltage at wich you set the transformer doesn't matter. You created a short circuit trough the oscilloscopes ground.
It is imposible to know if it is or is not damaged only from what you said. If it turns on and you can still measure with that channel it is probably fine. If it is damaged, you may or may not be able to have it fixed.
I would definitely recommend talking with your dad about what happened. He can help you determine if there is damage or not, and he deserves to know. Worse case, you made a mistake and have to pay for it. We all do, but at least you can make things right again.