I actually have this exact injury, except by the time my fracture was actually discovered, it had “set” somewhat incorrectly. I was a student at the time I sustained the injury and somewhat blindly trusted the health clinic I went to despite being in intense pain. The clinic did not suggest x-rays and I somewhat ignorantly did not follow-up at the time because I believed they knew what they were doing. I wish I had requested x-rays because I would have had more treatment options at the time; instead, the injury set on its own.
I don’t remember when I got back in the saddle. At the time I was just riding in school, and the fall happened fairly close to the winter break. I was probably back riding in a few weeks, but I was in pretty intense pain for a while. Eventually the injury did set by itself, but I experienced a pretty severe flare up that summer and sought additional treatment (at a different clinic this time!). Apart from pain management, they recommended physical therapy. They were not keen on my continuing to ride, but I continued after another short break that summer. The physical therapy focused on strengthening my core in order to support my back. This is the best thing I can recommend from my own experience - seek out a consultation or research some physical therapy exercises you can do to really build the strength in your core and surrounding back muscles. That was actually what helped me the most.
Other forms of low impact exercise like walking are good for strengthening, as well, and can really help. If you are currently riding, I would avoid doing any kind of jarring movement like sitting the trot or any kind of jumping work until you are farther along in the healing process.
It has been about 8 years since my injury and at times I initially found myself wondering if the pain was going to stay with me forever, but I am happy to say it has primarily faded. I do get some nerve tingling every now and then and I cannot stand for long periods of time without getting pretty bad back pain, but otherwise it is okay. Riding wise I am able to do just about anything and be perfectly okay (including sitting trot, etc.).
I don’t know about your particular injury but just wanted to respond since I also have a compression fracture in the T-12 vertebrae. Physical therapy and strengthening exercises, muscle relaxers and pain meds (only initially) and taking it easy on myself in the saddle were the things that helped the most. Now, just being aware of things like I described above (I have a cube job and try to remember to stretch now and then, etc. and I try to sit in chairs that have backs, etc - man I am an old 28 :winkgrin:) is all it takes to manage it.
Of course I have fallen in the years since but am VERY protective by default of my back. Just be selective in what you ride and don’t push yourself too far if you are experiencing pain. Good luck!