Most Helpful Guy
The silent treatment is childish passive-aggression, and something you should be well beyond by now, especially since you recognize it is a misunderstanding.
So, whether you misunderstood him (in which case you have no right to give him the business, it was YOU who misunderstood), or he who misunderstood you (in which case, by seeing it as a misunderstanding, you should be able to recognize, and forgive, his misunderstanding), it should not matter. You should be more mature about this. You should TALK, because COMMUNICATION prevents misunderstandings, and the silent treatment, by definition, is NOT COMMUNICATING.
And you should put his mother's health, and his emotional stress due to her medical condition, at least in this moment, as more important than your hurt feelings over what you admittedly recognize as a misunderstanding, and you should be there for him and sympathetic, not angsty and selfish.
Most Helpful Girl
... what do you hope to accomplish via giving him the silent treatment? Do you think you'll actually communicate anything, like being clear with which of his actions specifically didn't sit right with you, via telepathic measures?