Hi Alix,
Spasm is the body’s way of self-splinting to prevent a movement or action it has perceived as damaging and would like you, the human, to not repeat.
Now, for clarification please is it your entire right side of the back body that is in spasm or is it more localized than your post intimates? In order to look after it properly it would be helpful to get an idea of what is in spasm.
First the nutritional pieces. Avoid wheat, dairy, and refined sugars. Increase hydration foods which would include drinking water and eating more fruits and vegetables. No caffeine. The foods you eat now should be Yin in the body. No spicy foods please.
Next, anti-inflammation. Whatever you do to reduce inflammation in your body. Perhaps you take Zyflamend from the health food store. I prefer to brew up a turmeric beverage consisting of rice milk, tumeric, cardamom, a pinch of safron, and a perppercorn, brought to taste after cooking with some agave or honey. If you’ll actually DO this and do it twice a day then PM me and I’ll give you the exact instructions.
Asana wil be very difficult especially if you’ve pulled a deeper muscle like the Quadratus Lumborum. I would not, at this point, advocate Tadasana and Viparita Karani. Instead, Supta Padangusthasana with a strap. That will release the lower back.
For now you need to quiet. On your back please with knees bent. Exhaling, draw the left knee toward the right chest going two inches less than your full range at this point in time. Then inhale back to starting position and, exhaling, bring the right knee toward the left chest. Use the hands on the shin for the drawing action and keep the back body in contact with the floor, including the shoulders and back of the skull. Do 12 on each side and do this every half hour until you have some ease. Then once an hour after. This must be very focused work with the mind placed in the area of spasm and the breath directed where the consciousness is placed. The back body must be relaxed, grounded, and connecting with earth energy.
Additionally a warm epsom salt bath will be very helpful and frequent applications of massage oil to the skin to settle the nervous system. If you have organic, untoasted sesame oil use that directly on the area where you are having spasm. At least twice a day, once in the am and once at night before bed.
This is as much as I can give over the internet.