I can understand his being upset that Carly never told him he was the father. He should have known and been allowed to make the choice whether to be involved in her life or not. That was taked from him.
As far as telling others that’s not their business as it doesn’t affect them one way or the other with the exception of Chloe. Besides Melanie doesn’t know yet so how can he tell everyone in Salem before she knows. That girl has been through enough drama, disappontment and surprises that would drive anyone insane.