Unlikely that you broke the main breaker. First turn the main fully off and open the panel. Make sure there is nothing touching the bus bars, etc...

Turn off the breaker to the garage panel and the one you added and try turning on the main. Then try the others.
Divide and conquer.

Many breakers are designed so that, when popped, you must press the switch towards the OFF position before you can reset it. It may appear to be OFF, but it isn't quite there.

It could be that the breaker is bad, but not that you "broke" it. I have seen many, many main breakers that fail due to age and poor design simply from not being cycled.

Also, it is pretty much a certainty that you will not find it at a big box store, especially if it's more than 100A.
The breaker is not red, is it?

Good reason to leave electrical work to somebody that knows what they are doing.