Pain that worsens with coughing, sneezing or bending, together with it running down your legs, usually points to a disc in your lower back pressing on a nerve rather than a plain muscle strain. The weakness you're noticing needs a proper look rather than waiting it out, since nerve related back pain tends to respond better the earlier it's treated.
Next Steps
See a physician or orthopaedist for an examination, who can decide if imaging is needed. Until then avoid heavy lifting and prolonged bending, and gentle movement generally helps more than complete bed rest.
Health Tips
Go to an emergency department straight away if you develop numbness around the groin, or lose control over urination or bowel movements.