For years, scientists have used data from NASA's Kepler Space Telescope to look for and discover thousands of transiting exoplanets. In its extended K2 mission, Kepler observed stars in various regions of the sky all across the ecliptic plane, and therefore in different galactic environments. Astronomers want to learn how the populations of exoplanets are different in these different environments. However, this requires an automatic and unbiased way to identify exoplanets in these regions and rule out false-positive signals that mimic transiting planet signals. We present a method for classifying these exoplanet signals using deep learning, a class of machine learning algorithms that have become popular in fields ranging from medical science to linguistics. We modified a neural network previously used to identify exoplanets in the Kepler field to be able to identify exoplanets in different K2 campaigns that exist in a range of galactic environments. We train a convolutional neural network, called AstroNet-K2, to predict whether a given possible exoplanet signal is really caused by an exoplanet or a false positive. AstroNet-K2 is highly successful at classifying exoplanets and false positives, with accuracy of 98% on our test set. It is especially efficient at identifying and culling false positives, but for now, it still needs human supervision to create a complete and reliable planet candidate sample. We use AstroNet-K2 to identify and validate two previously unknown exoplanets. Our method is a step toward automatically identifying new exoplanets in K2 data and learning how exoplanet populations depend on their galactic birthplace.