If you get a blood transfusion from somebody else with the same blood type, does it mess up your DNA?

No, your DNA cannot be changed. There are stories of people who have had organ transplants suddenly having a change in, for example, what they like or dislike. For instance, I heard a story of someone who, before the liver transplant, hated hamburgers. After the operation, he loved them. Nobody could figure out why until the family of the donor mentioned the donor loved hamburgers. So, no, not your DNA, but sometiems weird things happen