I have a Nikon d3300 with 18-55mm lens. I bought 55mm Vivitar Wide Angle Lens and Telephoto Lens. And it won't screw on. Do I need an adapter?
If you look on the front of your kit zoom lens, you will see a marking with a number and a ⌀ symbol. This is the filter thread diameter — what front-side adapter lenses like the ones you bought attach to.
I believe that on the 18-55mm lens that comes with that camera, the value will be ⌀52. That won't work with the adapter lenses you bought. (I believe that some other 18-55mm lenses from Nikon did have a 55mm filter thread diameter, which may have resulted in confusing labeling on the things you bought.)
You can buy what's called a "52-55mm step up ring". The link goes to a generic one I can't vouch for but should show you the general idea and price ($7).
However, be aware that these type of front-mounted adapter lenses are basically toys. They will introduce significant optical flaws into images taken. The telephoto adapter may actually be worse than just using your lens at 55mm and cropping to simulate zoom. Of course, you can't do that on the wide end so the wide adapter may open up new possibilities, but it's really no substitute for a real wide-angle lens.
See Can screw-in wide angle adapters/converters produce decent quality results? for more on this.