I'm not well versed on the historiography of (or even the approach to) contemporary history. I've also had professors express to me that unless it happened 40 years ago it's not technically history, but I'm curious about the field (if it even exists in the way that I'm thinking it does). If 'contemporary history' is too broad of a topic, I guess I'm more interested in a general political and social history of the present day.
Contrary to what your professors have said, history is still history if it happened less than forty years ago. My entire PhD dissertation goes from the 1980s to the early 2000s. The opinions expressed by your professors are in the minority, although there still is a bit of a stigma to recent history. If you're interested in the methodology of doing contemporary history you may want to check out the book Doing Recent History.
Most contemporary history starts in the recent past and goes up to around the present day, attempting to provide historical context for the contemporary world. Beside political and social history, what subject/area are you interested in (U.S., European, global history, human rights, war and society, etc.)? Since you're into contemporary political history, you should check out Sean Wilentz's The Age of Reagan. He lays out the benefits of contemporary history in the beginning of the book. Other good historians focused more on Europe include Timothy Garton Ash, Tony Judt, William Hitchcock, and Mark Mazower. This is only a very short list, so let me know if there are other historians you may be interested in.
Edit: Daniel T. Rodgers' Age of Fracture is another good one. It recently won the Pulitzer and Bancroft prizes.
An historian who focuses on modern times (and can be found all over the news around presidential election season) is Allan Lichtman, who is famous for his Keys to the White House.