I might have swallowed a small piece of glass (about 2mm length by 1.5mmwidth by 1mm thick). What should I do?

Nothing. A sharp object like a needle or chicken bone that gets stuck in the esophagus needs to be retrieve by endoscopy due to the risk of perforation of the esophagus. If the piece of glass was truly only 2 mm x 1.5 mm it's not likely to get lodged in the esophageal wall due to it's tiny size. It should pass out of your body with your stool. But it you develop pain must see Dr asap.
Good....it's tiny. The good news is potentially harmful foreign objects that are accidentally swallowed pass through the GI tract (in 4-6 days typically) without complication about 80% of the time. 20% require endoscopy (removal by scope) but very unlikely in this case as piece is so small. Drink, especially, and eat generously so the speck will be moved along/cushioned. Rarely is surgery needed. Good luck!