Well, to know for sure you have to see a doc. That being said, if you definitely felt or perhaps even heard a 'pop', I doubt that this was just a muscle strain...
If it is a disc prolapse, which can make a popping sound accompanied by a sharp pain you should go to a doc as soon as possible and don't try to deal with it on you own. You could end with a herniated disc and that will not only hurt but may include pareses etc.
If one of the facet joints of the spine is forced though a range of motion it isn't designed for, for example because you roundbacked uneven (torsion), it may make a popping sound too and this hurts as well.
And lastly there is the illiosacral joint which hurts like hell when blocked, fortunately this is a 'stiff joint' with only a couple of mm of ROM so it is not a big deal, although painfull. Once unblocked the pain will disappear immediately.
So were exactly is the pain in the lower right back? How is the ROM of you spine, can you bend to the same degree sideways, forward, backward?
As a first aid I would recommed to rest 30min in the psoas position as often as possible.
Heat for example via a hot tube may be good as long as it doesn't make the pain worth. When I had a herniated disc I couldn't stand icing it for a single minute. Use what helps and doesn't aggravate the pain and let somebody check it.