Yes, it doesn't seem like you have quite enough experience to be doing this!
However, the first order of business is to replace the fuse and restore proper protection. If you would have done the repair correctly the first time, you wouldn't be in this situation now! And don't use the Hakko to solder on itself, if that wasn't already obvious.
But beyond that, I think the next area to look at would be the primary side of the transformer, specifically the connection that you pointed out was shorted to that temporary wire. You may need to remove the transformer completely if there are PCB traces on the other side that need to be inspected, or to get a better view of the transformer. Then continuity test the transformer windings looking for an open. If you're lucky, maybe a wire coming off the transformer windings going to the connection pin will be melted open and you could repair that. Most likely you will need a new transformer, though, since rewinding a transformer is expert level.