I have a Nikon D3300 camera. And I bought a 55-300mm Nikkor lens — but this lens is not an autofocus lens, so when shooting I must manually focus, and sometimes the photos are blurry. Is there any component that I can use to transform the manual lens into an autofocus lens?
The Nikkor (i.e., Nikon-made) 55-300 is an AF-S lens and should autofocus on your Nikon D3300. Why you think it's manual focus only, I'm not sure.
If the lens is a Nikon-made one, but designated as AF, that doesn't mean it's manual-focus only--just that it will only autofocus on a body with a focus motor. You'd need to get a D7x00 or higher end Nikon body to make it autofocus.
If the lens is a 3rd-party non-autofocusing lens that does not communicate with the Nikon mount, there is no way to turn it into an autofocus lens. Autofocus requires electronic communication with the camera body, and (on a D3300), a focus motor. There are hardware elements that you cannot DIY and retrofit into a lens without a great deal of expense, trouble, and expertise. And most of us would count the cost of a new Nikkor 55-300 lens as a much easier solution. (see also: Do separate autofocus motors exist for entry level Nikon DSLRs?)
As for your photos being blurry, it may have nothing to do with your autofocus, and could be due to the shutter speed you're shooting at, or your handholding technique. Longer lenses require more care not to blur when used handheld--you may require a tripod or monopod.