Rodents at night

I woke up last night with the feeling something was sniffing my hair. My room is so dark and quiet that sometimes I cannot tell if it is a dream or if I am awake. I thought maybe it was a ghost, that surprisingly comforted me but then logic slowly rolled in yet I refused to think more deeply into it. I settled on believing it was a puppy and dreamt of that for a while. Then again, something awoke me, I felt it. Something large was on my pillow by my head and what must have been its nose in my hair. I froze for a minute not knowing what to do. What if it bites?
I ran as fast as I could to the light switch and alas, I found nothing. I believe it to be a large rodent and it is taking up the same space as I am. At 4 am I found it nearly impossible to go back to sleep despite my drowsiness. I left the lights on, put on a movie, adorned my head with a thick wool cap and buried myself under my sheets.
What does one do when they find the rat I wonder? Am I supposed to kill it with my bare hands, or gently ask it if it would not mind living outside or in the barn next door. I am not sure if I can sleep soundly until I find the creature. I left a metal rat trap out with a cookie inside but I feel bad if it goes for the trick. The trap looks terrible and inhuman. And then, when I come home and it is in there, possibly still alive how do I free it from the metal jaws and where shall I put it?
Oh dear creature, I wish that you never stumbled into this house for we cannot be together but I must stay.