lied and then told the truth to a friend

My friend was in a mental crisis situation last night. I had tried telling him that he needs to call a helpline or call me, but he did not respond to said messages. I told a friend(2) who is also close to him about it, being incredibly worried for his health and safety. I convinced my friend(2) to talk to my friend (as per the guidelines of suicide prevention: connection keeps people alive). Nether of us told my friend that the events were connected, naturally worried he wouldn't be receptive, or worse - get angry.
Today my friend messages me frantically asking whether i'd prompted my friend(2) to talk to him yesterday. He seems incredibly paranoid about how many people know of this and angry. Naturally i was scared - would he feel worse or better knowing the truth now? I came clean and explained how much I care.

I don't think he grasps how much people care about him, partially on purpose - so he can feel worse about himself. I'm not sure i CAN convince him of the truth.