There is another rare side effect from the Johnson and Johnson vaccine; a neurological disorder called Guillain-Barre syndrome, which is not uncommon after infections. “To me what makes sense, if you are a woman, probably don’t get the J&J vaccine. Maybe get one of the mRNAs, because we havent seen any side effects. These vaccines work so well that they gave us excess protection, more than what we needed,” said Dr. William Petri, an epidemiologist at UVA Health.