Generally speaking, if you are chronically congested, which it sounds like you are, this will lead to inflammation and friability of the tissue lining your nasal passages. Therefore, when you blow your nose or otherwise manipulate your nasal passages, you are likely to cause some minor damage to this delicate tissue, which explains the small amounts of blood you are seeing on your tissue.
These small amounts of bleeding
are, in and of themselves, not likely to be a big problem. The caveat of course, is that you experience frequent nosebleeds or ever are bleeding and having trouble getting it to stop, then you need to see your doctor
More importantly, however, you need to get some medical help figuring out what to do with this chronic morning congestion. It is likely that you are suffering from chronic nasal allergies or chronic sinus congestion, and if you can treat these, the congestion (and bleeding) should go away.
I suggest that you start by scheduling an appointment with your primary care doctor
. They can examine your nose and throat and confirm a diagnosis. After that, they can help you decide which medications you might need to take to get the symptoms under control.