Nose bleeds (epistaxis, as it is called by doctors) are an unfortunate problem that is incredibly common. It is also common to have seasonal variation in the amount of nosebleeds that occur, with most people complaining of them more frequently during the winter, when the weather is cold and the air is drier. Cold and dry predispose the nose to bleeding
more by drying out the mucous and gentle tissues of the nose at the front of the nose. It is in this area that most nosebleeds occur, as it is where blood supply from multiple areas comes together, meaning that it has lots of blood.
Additionally, the front of the nose is a common site for trauma of all sorts. When the mucosa is dry and friable (meaning readily injured), it is a perfect setup for a nosebleed. It could be that you have bleeds more frequently in the spring because you are outside in the cold more often, even though it is not quite as cold. Alternatively, the allergies you describe could be causing you to rub your nose more frequently. Either way, if they continue or are serious, or are associated with any other symptoms, please discuss them with your doctor