Is it bad that during a nose bleed when I tilt my head back it feels like I am swallowing blood?

No. It is not unusual to feel blood in the back of the throat during a nosebleed.
Wrong position. When you have a nose bleed, you should pinch your nose with your thumb and index finger and tilt your head forward and not backward. Tilting your head backward will just allow the blood to keep running to the back of the throat.

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