If there is no structural damage (slipped disc, fractured vertebrae, partially torn ligaments), chances are this is muscular. Muscles in the back can contract very forcefully I’m a split second when a person or animal takes a fall or slips or lands badly. This is a protective reflex- the body tries to protect the spine bc the spine is so very important.
The problem that can arise (and often does) is that the muscles might stay contracted even when the danger is over. This can result in “muscle knots” and local muscle inflammation. Inflammation and very tense muscles take up more space than relaxed muscles. There is barely any spare space around the spine, so there will be extra pressure on the nerve roots and blood vessels in the area, and this in turn will interfere with nerve signalling and blood flow. This is how nerves can become pinched even if the cause might be all muscular.
Did you get any anti inflammatory med for your bun? (Meloxicam, loxicom, metacam and other brand names).