I was diagnosed with lower back pain two weeks due to a gym injury. Gave it 2 weeks rest, still pains after even light exercise. Solution?

Need more time. It may take much longer to get better. Physical therapy may help.
Rest. If have radiation of pain to lower legs or any changes in urinary or defecation functions or coordination of legs these would be red flags showing need for immediate attention. Otherwise heat and rest. If pain does not improve see an osteopath for diagnosis and imaging studies.