Yes, on New Year's Eve you can enjoy a fireworks show in Antigua, especially in tourist places and where there are more hotels. Usually, hotels and restaurants, offer as part of the entertainment to their customers, a fireworks show to celebrate the New Year's Eve dinner.
Ask the restaurant you chose for your New Year's Eve dinner, or the reception of your hotel and they will be able to tell you if the fireworks show is part of their plans. Also, check out the best restaurants in Jolly Harbour.