"Next week" and "yesterday" are times in relation to now. However, in reported speech you are talking about times in relation to that point in the past (when the person spoke). To answer the question, it's possible to use "next week" if next week in her quote is next week in the present. It makes sense. However, be careful of allowing yourself to be confused by present or future situations when using reported speech - this is where most students go wrong. Reported speech sentences are still fixed in the past.

"She said that she'd come to my party next week" is perfectly fine. Maybe some grammar teachers would frown upon it, but it's fine for everyday use. The only situations in which I'd suggest not using it would be ones where "next week" is no longer the real "next week". If I'm telling someone what she said a month ago, for example, I'd use "the following week" because then "next week" in the story and in reality are different weeks. Yesterday works very much the same. Hopefully that helps.