First I would stop "blowing hard" into your nose. If you can't clear your ears with a gentle blow then something is wrong. Forceful valsalva has been known to cause your ear drum to rupture if you are not careful. You may have a sinus infection/allergies or some other problem. If your ears clear, then you must have all of the plumbing in the right place so I would look at a sinus blockage. The blood coming out at the end of the dive would tell me that you were experiencing a reverse sinus squeeze. Do you feel pressure/pain during your assent? Try clearing your ears prior to diving to ensure that everything is moving the way it should. The air should go in as easy as it comes out.
Rob