If you are considering graduate school, a few thoughts are in order. CSB/SJU's Career Services has information available here.
First, distinguish between PhD work in the Arts & Sciences from graduate professional education (JD, MBA, MD etc...). Some fellowship programs are only available for those interested in a particular field or program type. Additionally, many programs have restrictions whether the fellowships is tenable for work towards a Masters degree (MA, MS) or PhD (doctoral) work, so read the rules carefully.
Second, be sure you want to apply to graduate school! Before you apply, you need to have a clear idea of what you want to do with the degree. Additionally, particularly for applications to academic PhD programs, you need to articulate a clear sense of what the field is like, where it is heading and what you hope to contribute. Talk with your professors, advisers, parents and friends both before and while you apply to graduate school. The more you can clarify your identity and interests in relation to your chosen field, the more effective your application will be and the more likely you will be admitted to the program(s) of your choice.
As you think about graduate/professional school, be aware that there are many programs available that can help fund your education. Most of these programs have deadlines in the fall, specific field/degree requirements or contain service obligations.