During Shivah Nikiyim, is it a problem to find blood on my pillow case? I am pretty sure that it is either from my nose or my ear.
In general, since one moves around during sleep while unaware, and similarly, can move around the pillow and blanket during sleep while unaware, one cannot be lenient on this basis alone. [YD 190:14] For example, it is within the realm of plausibility for someone to move the pillow between the feet for better support, and then move it back to the head, all while asleep or half-awake, without any recollection the next morning.
However, if you were wearing underwear the entire time that you were in bed, and they are clean, that is an acceptable basis to be lenient.
Similarly, if you know for sure that you had a nosebleed or were bleeding from your ear, contact a Rav regarding those details.