Hello Sophie! These two prases "a spitting image" and "a carbon copy" would normally be used (in the context of the sentence) to say that two people look alike or are very similar. And these similarities could be because of genetics or family ties. If you are talking about someone who is the same as someone else in a professional way (as in a Dr.) then I would say "replica" which also means a copy or model of something. or "duplicate" which also means a copy of or a recreation of something. So the sentence would be written like this: "People expected me to be "a replica"/"a duplicate" of their last physician, and they were upset when this wasn't the case I hope that helps!

I would say that "A spitting image" refers to appearance. The latter, "A carbon copy" refers to something in its entirety. In the case of your example, a spitting image of him would be to simply look exactly the same as him. A carbon copy of him would be to be just like him, traits and all.

Maybe "just like" with no "of" ?

For that phrase it is a spitting image. = same as a double-ganger in German. The English spelling or "doppelånger" German a lookalike. Carbon copy comes from the term a carbon copy = from the carbon paper that make carbon-copies. We used to make copies of what we wrote by sticking dirty black carbon paper between two sheets of paper, before copier machines were invented. So people have began to use the two terms interchangeably, but a carbon copy is a different concept. copy-duplicate or replicate: https://writingexplained.org/replicate-vs-duplicate-difference