If you have done your back, it is best to stay active, rest only weakens muscles and allows them to stiffen.
If you have a back problem, then you do need to think about core training, that is exercise that specifically targets the core muscles that support the spine. Pilates is an effective exercise as is belly dancing which I do, dancing is more fun than exercising and with thirty giries around me, what an enviroment to exercise in.
I have a weak back, caused by slipping a disc twice, one time above the vertabrae and a few weeks later below the same vertabrae, an injury picked up in industry, caused by lifting a light object out of sucking mud on a construction site and the second time, well,er with the ex.
But core training you need if you have back problems.