The "this time of year" part could be a red herring. Common nosebleeds are generally the result of an irritation to the septum -- dryness, scratching, trauma, inflammation (virus, allergy) -- or simply an anatomic situation where you have vessels that are too close to the surface and easily break open. The easiest thing to try yourself is to get some saline nasal gel (not spray) and apply that liberally. Some medications, like aspirin and ibuprofen can enable bleeding to occur more easily too.
Yes, but they started a couple of weeks ago. This has been going on for a while. They happen in the morning, and go away with a little pressure for just a few seconds.
Do you have allergies irritating your nasal passages?