Back sprain or strain, usually caused by injury to your back muscles, takes about a month to recover.
The initial severe back pain in the first week after injury will gradually be replaced by a nagging back ache usually in the mornings and after prolonged sitting for 2-3 weeks, before subsiding to residual lingering stiffness for another 2-3 weeks as your back muscle slowly but gradually and naturally heals.
Pain medications, physiotherapy, chiro, TCM are optional and not needed in every case (although may help to ease pain temporarily). It is important to rest and care your back, avoiding physical strenuous activities and prolonged sitting during this month or else your recovery will be delayed and your pain will not improve after a month.
Despite doing this and your pain still persists more than a month, a more serious diagnosis (e.g. slipped disc, fracture) other than back sprain/strain must be suspected and further evaluated - usually by MRI scan.