Lens for my Nikon D3300?

I am using this camera for a variety of purposes (videos, nature photography, sport photography, etc), so I need a lens that will be fit for all of them! Right now I am using the lens that came with the camera, which is a DX VR AF-S NIKKOR 18-55mm 3.5-5.6 II. It works alright, but for me, I need something with greater zoom capabilities. I am looking at getting another lens with a max focal length of 200mm. I am a college student (film school), so I do not have a ton of money to spend. Basically, I am wondering if I would be better off getting an 18-200mm lens and selling my 18-55mm lens, or just getting the cheaper 55-200mm lens and keeping my 18-55mm lens as well. I know there are tradeoffs in both scenarios, but the bottom line is that I need a lens with better zoom capabilities. I am on a budget, so I don't have many options, but I feel that one of these two would be my best bet. Please give me some advice as to which direction I could go and any suggestions are appreciated!

Read more: Lens for my Nikon D3300?