Yes, Home Depot and Lowe's both sell a touch-up kit. If your sink is like mine, it is ceramic and you'll need a ceramic touch-up kit.
Madame's sink may actually be ceramic coated (most kitchen ones are, if not stainless-steel). She can use the same kit. If the scratches and damage is really unsightly, they also make a kit that coats the entire sink and looks great when done. It's not quite as durable as the original ceramic coat, but works well and easy.
Like Stoneman mentioned, if it is the bathroom ceramic sink, they are really cheap at Home Depot and easy to replace (or have replaced). If you can handle a screwdriver, some glue and make a few props to hold the sink up while drying, you'll have no problem.
2003 Alpine 40FDTS (400HP)
Long Beach, CA