Trailer tires don't wear out-----they AGE out. Yours is OLD and needs replaced.
"I did not adjust the brake on the wheel I took off, since I didn't change anything"..........sure you did. You had to back off the brake shoes to pull drum (or they weren't properly adjusted prior too).
So a few things......need to pull that wheel/hub and check for grease in brake area, properly install/adjust bearing play and then adjust the brakes not only on that wheel but the others also. (Jack wheel up, tighten star wheel while rotating tire until tire stops. Then back off star wheel until tire rotates with a slight drag)
And why didn't you check the other wheels....bearings/brakes???
One position doesn't mean ALL good