Strain/strain is likely the correct diagnosis, however; it's not always the muscle strain itself that creates the extreme pain, it's how your body is reacting to it (inflammation, muscle spasm, etc.) This process may ramp up and take a few days, sometimes. Sometimes, it starts getting better over time, but the dysfunction is still there and your body makes a "workaround" movement pattern, just to get by. This has likely happened before, but maybe only resulted in some soreness and maybe not pain, so your body adapted (workaround). A "workaround" is when your body figures out how to make it work, using what it has, even if it isn't optimal, kinda' like using duct tape to hold it together, but doesn't fix it. Chiropractors sometimes call this "subluxation", osteopaths call this an "osteopathic lesion", but that's another topic.

Unfortunately muscle strains can be pretty painful. The pain meds and anti-inflammatory pills, etc. are to decrease that process from happening and may address the symptoms, but you need to ask yourself why it happened? Did you injure yourself while working out? It may be one specific incident, or a lot of little ones accumulating to end up where you are. Chiropractic care can help with both causes.

Muscle spasm is what is causing your torso to "lean". Your muscles are protecting themselves from getting strained again (splinting), but may be "over reacting" a little, the meds can help with that, but doesn't fix the dysfunction. The meds may help you get through this, and may allow your body to do a workaround again (patch itself), but set itself up for it to happen again, or it can heal on it's own, possibly, and maybe not optimally (a "functional workaround").

The reason it may have happened in the first place is because when you needed your lower back to do something, it just didn't move when it was supposed to (possibly due to a "workaround"). This made another part of the lower back have to work much harder to do that motion and was too much for that area, which injured that part. After the injury, they body responded. It has probably been progressively getting to this point, if it wasn't a specific injury.

Chiropractic care would be very helpful to fix this while you are healing as well as make sure it moves well enough to prevent future issues.

If you're wondering how chiropractic could help with a strain/sprain, think of it this way. If we can adjust the spine so it can move better, it can allow the other segments of the spine to "help out" as needed, which puts less stress on the already injured area. You probably developed this problem because when you were working out, your back needed to have "assistance" and coordinated movement from other parts of the spine (coupled motion, etc.). It didn't do that, possibly because of overlaying "workarounds" that your body figured out to use to do a certain motion and it just couldn't withstand the demand and got injured.

Chiropractic care can help it move better, allowing more coordinated movement and ability to disperse the physical stresses on it by adjusting it, possibly some therapy, too. After that, the more you "use it" (correctly), the more your body will adapt to a more biomechanically optimal movement pattern which allows your body to use the areas of your spine when called upon to do so. I hope that's not too complicated an answer, but if you know how you got there, you're less likely for it to happen again.

I would encourage you to wait to work out again until you are able to work out with good form, not before then otherwise, you "re-write" the muscle memory and movement pattern, like practicing something wrong, and it will set you up for it to happen again in the future by reinforcing bad biomechanics. When you start working out again, start out with less weight and ramp up until you can go back to where you were. Make sure your form is good with the amount of weight you are using. Ask your chiropractor to advise you on how to work out correctly if you're not sure about form.