Shakespeare did not win any awards. He didn’t, mostly because there were not any writing awards in his day. Shakespeare is still winning awards now for his work, but it is mostly his plays because people are still presenting them now. Some people are winning awards for what he wrote, even if everyone knows that he wrote certain stories.
Shakespeare, was a playwright, and he wrote for the most prestigious company of actors that has ever been, therefore he was only interested in providing the sort of materal they liked to present to an audience, His reading was quite something, as he was able to read French, Italian and Latin, as well as English, so he compiled his plots from a number of reliable sources among Roman, Greek, and other well established authors of note, which gave him the necessary information he needed in writing his plays. Other playwrights also contributed, and the theatres were able to provide a constant supply of fresh, new material every day! Shakespeare probably never thought about awards, as none were available at the time he was writing. Others, such as Marlowe and Webster, received no such thing as an award, although they most certainly deserved them, however, he did receive recognition, from his Sovereign, Elizabeth Tudor, his professional contemporaries, and the new king James 1, who awarded the actor group four yards of red linen to drape over their forms at his Coronation! This is the only "award" he received in his entire lifetime!