Problems with tile to floor at doors

Hi
I was wondering if someone could advice me regarding this problem which is due to tiling new tiles over old tiles. The reason this was done as had two burst pipes before and didn't want to take the risk of it rehappening while removing the old tiles. However now completed we have the problem of approximately 1-2 inch drop from the now raised tile at the bottom of the door into the next room. We were able to have some doors shaved at bottom which was grand but the drop is evident at the bathroom , and two bedrooms. Is there a door trim that can be applied to these drops as the doors in these areas can't be shaved as would appear even more rediculous as adviced by the joiner. Any advice would be so appreciated.I hope you see photo attached.

 

Thank you. I've a feeling that's what will have to be done.

 

It looks bad and an ugly sight without doubt. But I'm sure something can be done as KIAB suggested. .