Thanks for all the advice everyone! I'll try repositioning it first to see if that helps. If not I guess I'll go back to the old one until I can afford something nicer. The saddle is just as wide as my old one and significantly less padded, so I'm betting it's either the shape of the nose or how it's positioned.
Unfortunately cycling shorts won't do in this case - I commute by bike and have nowhere to change at work. But I'll definitely keep that in mind for longer fun-rides.