It Was Supposed to Be Worse
When turning a book into a movie, it’s nearly impossible to keep all the details from the book. Eagle-eyed fans will always find differences (some minor, others major) between the book and the movie. As some people pointed out, Peeta’s wound in the book is very different from what was shown in the film.
The author, Suzanne Collins described it as a big cut that went down to the bone. Eventually, it had to be amputated and was replaced by a prosthetic leg. In the movie version, it wasn’t too bad to begin with and almost healed completely after the medicine was supplied.