(1) It wasn't her discovery. The critical x-ray image of DNA was taken by Raymond Gosling in Franklin's lab nine months before Watson saw it. She had plenty of time to submit a paper if she understood the implications of that photo. She did not do it.
(2) She has received credit for what she actually did, which was to run the lab where that critical photo was taken. Franklin's contribution to the discovery is extremely well known. She and Gosling published an article on their DNA images in the same issue of Nature that contained the Watson-Crick article.
(3) She did not share in the Nobel Prize because she died in 1958. Watson and Crick received their Nobel in 1962. The Nobel Prize is not awarded posthumously.
When Watson and Crick saw that x-ray photo, Franklin was already on her way out of King's College, moving to a different job where she would not work on DNA.
She made her contribution, but she did not discover the structure of DNA.