|My well-used knives: 10" Chef's, Santuko, paring|
Paring knives are small knives with a pointy tip. You should be able to pick one up cheaply. Many kitchen stores even give away paring knives when you purchase a decent chef's knife.
People often think that dull knives are safer than sharp knives. This is untrue. A dull knife is still absolutely capable of doing a lot of damage to your fingers. But, because it is dull, you need to push a lot harder to get it to cut through food. This extra force makes it more dangerous. It can bounce off food when you least expect it, ending up in your hand. Sharp knives require almost no work to cut through food. No pushing, no whacking, no forcing. Keep your knives sharp and respect that they are sharp. You won't have to work as hard in the kitchen.
We recommend that you find someplace that will sharpen your knives. Our local hardware store sharpens knives, as does some of the supermarkets. You won't need to sharpen them often - maybe once or twice a year depending on how much you use your knife - but you'll be happy you did. It's also important to steel your knife, to keep the edge really sharp. Here's a short video from Alton Brown that distills steeling and sharpening down to its bare essentials.