What a terrible burden for you. Of course you had nothing to do with your brother's illness. In all likelihood, you were one of the few allies he could rely on in childhood, one of the few safe places he could check in without anxiety.
Children feel responsible for events that are completely out of their control. You did not make your father choleric. A spilled thermos is not a disaster, but a furious out-of-proportion punishment is a disaster. It is a disaster for a child to constantly fear that such punishment awaits even for trivial offenses. This cloud a child lives under helps to shape worldview.
I speak from experience. I had a 'choleric' father...that is a euphemism. He was horrible. I lived in fear of him. We all did. This certainly contributed to an inordinate cautiousness I evince even today. Of course, having such an unreasonable parent also led me to question authority. For that I am grateful :)
Let yourself off the hook, dear kadna. Your father caused you to tell that minor untruth. Fear of punishment was so great that you were paralyzed into silence.
I hope your brother has weathered his trials well over the years.

Something we share (with a lot of people!): intemperate fathers.