Previously you've "looked backwards" in time by using an article's references, but now you want to go forward. To do this, you will use the Web of Science, a subscription citation index available through the Library.
A citation index is a particular type of bibliographic index (e.g., the bibliographic databases you've searched before - PubMed, Academic Search Premier, etc.), that allows you to easily discover which more recent documents cite which older documents. So, while a journal article's list of references allows you to see older cited sources, a citation index allows you to find newer sources that cite your original journal article. In other words, Web of Science allows you to find your article in another article's bibliography.