It sounds like the inlet has broken loose from the heater core. The only real way to fix this is to remove and fix the core. You could probably cobble up a temporary fix with the silicone, but it sounds as though it's been leaking a while and you really don't know what the core itself is like.
I don't know if you can remove the core without removing all the heater housing from the firewall. That involves almost removing the fender. When ours came loose we had the entire front end off.
I would also recommend you check your front passenger floor for damage.