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.0
Most Helpful Girl
Don't give him the silent treatment, he obviously needs you right now. Show love and support, if he can't depend on you during this time he will probably realize that and leave you and then your silent treatment would have been a waste of time anyway. I'm sure you two can talk about it like adults.0