Hi, there. Allergies can indeed cause nasal bleeding
, though usually it is not profuse and will stop easily, as yours does. When the body develops an allergy a common symptoms is rhinorrhea (runny nose). Because the fluid flowing past the lining of your nose is very watery, is basically leeches fluid out of the cells in this mucosal lining (a process called osmosis). Constant irritation from rhinorrhea, blowing your nose, rubbing it, etc. all cause this already dried out tissue to break and tear easily. Over a certain period of time this can lead to bleeding, since the blood vessels in the lining of your nose are very superficial and close to the skin. In fact, over long periods of time your body can even begin to develop thickening of the lining which can lead to polyps.
The bottom line is that in just the same way you may need to put lotion on your skin when you live in a poor climate, you need good mucosal care too when it is in the hostile environment of allergies. The first thing I would suggest is saline sprays. This helps to even out the osmolarity of the fluids so that the fluid in your cells does not get sucked out and dry out the tissue. In addition, make sure the humidity in your house is sufficient. You may want to buy a humidifier if you don't have one built in. And lastly, get your allergies under control! If you have not already, you should see an allergy specialist. There are a number of treatments available and you get help finding the one that works for you.