Of course you can care. What you did is perfectly fine.
Just try to remember that the grieving process for you is different than for other people. While you might say "Am I not supposed to care?" they might say "Why would I care about someone I don't know and bring myself down like that?" Some might even use humor, while such a tactic might seem completely tasteless to others.
Also, as odd as everyone might seem to you, you might seem to them for reacting in the way you did. Unfortunately we're just going to always be in the minority on that one :/
Just try to remember that the grieving process for you is different than for other people. While you might say "Am I not supposed to care?" they might say "Why would I care about someone I don't know and bring myself down like that?" Some might even use humor, while such a tactic might seem completely tasteless to others.
Also, as odd as everyone might seem to you, you might seem to them for reacting in the way you did. Unfortunately we're just going to always be in the minority on that one :/