Liv - hate to tell you, but Uggs are actually made from sheep skin. The outside was the inside of their skin, and the inside was the outside of their skin. I think even if you order the woven ones they have, which maybe you did, the bottom still has fleece, but I'm not sure. Even if it was wool, which I think may be what you were thinking, while taking wool from a sheep doesn't kill them, it is generally far from a kind practice. It is often not done very gently and the sheep gets cut up because of it. (I am qualifying this because there may be so-called humane sheep shearers, but that is not going to be the vast, vast majority)
I looked at your profile, and you're very young. I only mention this because there is a lot to learn about being vegan and it would be a shame for you to become overwhelmed at any point and give it up. Generally, most people who 'label' themselves 'vegan' don't buy animal products of any kind - including clothing made from animals. However, many people who become vegan do continue to wear the items they already had that were made from animals. That would be wasteful to get rid of it (unless you decide to donate it). I consider myself a hardcore vegan, but I do still have some leather shoes and wool sweaters that I will continue to wear until they are worn through. Every time I wear them I am reminded of why I went vegan and it just strengthens me, so I don't live my life with guilt. However, I will not buy any more.
Now, like I said, don't let that overwhelm you. The fact that you are trying to eat vegan at such a young age, all on your own, is really amazing. Just keep up with it, and as you learn more and grow older you can incorporate more vegan ways into your life.
If you ordered your Uggs from a place where they are easily returnable (like Zappos), you may want to consider returning them and replacing them with a kinder option. If not, you can always seek to make to make kinder purchases in the future.
I still have one pair of velvet Doc Martins that I will wear, even though they contain some leather. I also have a pair of jeans that I removed the leather patch from that I wear. Like Hazel, I won't buy leather or silk again in the future (I'm allergic to wool, so I never bought that), but there is no point in wasting what I already have.
My favorite vegan shoe store is http://www.alternativeoutfitters.com/. It's a great place to shop because they have really cute, fashionable shoes and they have already taken the guess work out of whether or not they are vegan. They also have a fantastic selection of coats, scarves and beanies at the moment for winter. I just checked and they also have vegan uggs for less than $50: