I'm going to disagree with most of the previous posters. I think yoga would be disasterous for your back right now. I train a few clients whose problems sound exactly like yours- one is a surgeon ( standing, slightly bent over most of the day) and the other works in a medical lab (standing, slightly bent over most of the day.) You probably have a lot of inflammation going on there and the yoga will make it worse until you've healed and strengthed.
My suggestions are
1) ICE your back for 20 minutes each evening when you get home from work. OK, I know this isn't pleasant. Use a bag or two of frozen peas and cover them in a kitchen towel.
2) Avoid exercises that put you in the position that caused the pain in the first place. No bent over rows, no top loaded squats (yet), no impact cardio or plyometics.
3) Work on lower back and ab exercises that don't "bend" you: forget crunches and v-ups, and do planks instead. Hold you abs really tight. If you have access to hanging ab straps or a captain's chair where your back is supported, do those. Strong abs=stronger back. Supermans are good- again, keep your abs tight.
4) Did I mention ICE?
5) Do you have access the cable equipment? If so, do mid-back rows on cables set at chest height. You want to keep you chest out and your abs tight as you pull whatever handles you choose towards your chest. Don't lean into it. That's what causes the problem in the first place. If you don't have cables, get some bands abd hook them on something at chest height to simulate cables.
6) Stay off of balance equipment (bosu balls, wobble boards, balance discs) until all pain is gone. These are great tools for strengthening your core muscles, but if those core muscle (the small muscles of your lower and mid back) are inflamed, they will make the condition worse.
7) ICE after your workout. Ouch...sorry!
8) I agree! Take stretching breaks
Mel