Rear break dragging when hooked to a trailer

I drive a 2010 F150
Recently (within the last year) when I haul a trailer
with my truck the rear drivers side break is
dragging. I have thought it was the trailer breaks,
my brother had said if the wiring was opposite (east
coast vs west coast) that may cause it. However,
this isn’t a problem I have always had and I’ve had
the problem with a trailer I was hauling somewhat
regularly then the problem just randomly came up.

I now have a new to me two horse trailer, I did take
the truck to a mechanic two days ago, they said I
had a blown fuse and relay, replaced it, all was
good yesterday and this morning hauling the trailer.
This evening taking the trailer home from a friends
house the locking up happened again, I babied it
Home and smelled heat near my rear axel not the
trailer, my rim was also hot and the trailer tires were
not. Passenger side was also not hot. What the hell
could this be? Thanks in advance for any help.