PHS241 wrote:

Both forms, I think are correct

Yes, but they mean different things.

PHS241 wrote:

but how would you try to explain "had had" to someone learning english?

Like this: "had" refers to a specific time in the past. (e.g. She had an injection on January 3rd.) "had had" refers to an unspecified time BEFORE a specific time in the past. (e.g. By January 3rd, she already had had an injection.)