Nothing is grammatically wrong with placing and
or other coordinating conjunctions at the beginning of a complete sentence, although this practice should be used sparingly. Novice writers should be especially careful not to begin sentence fragments with conjunctions.
Incorrect: We hung the wallpaper and painted the wall. And laid new tile.
Correct: We hung the wallpaper and painted the walls. And we laid new tile.
Correct: We hung the wallpaper, painted the walls, and laid new tile.
Although the second sentence above is technically correct, the third sentence is preferable because it is less wordy and flows more smoothly.