I woke up with a burn blister on my side

You may have got a friction burn and didn't know it.  When something causes an abrasion like a rug burn, it can potentially become a blister. Are you sure if it is a "burn" blister?  Sometimes a person may develop a blister if he/she has a reaction to something.  Do you have any clue as to what may have caused it?  What does it look like? Is it reddened or does it just look skin-colored with yellowish fluid inside? If it is reddened, it is from an apparent abrasion of some sort.  If it is the latter, you can bet you may have a skin reaction to poison ivy or some other irritant.