Maybe see a chiropractor? I had never seen one myself until just last week. I decided to see him because I hurt my back weightlifting and he also runs a weightlifting gym and is a powerlifting competitor so I figured if anybody could tell me what I did to myself and how to fix it it would be him. My own doctor would say exactly what yours did: rest, ice, ibuprofen.
I hurt the ligaments in my back but not my spine. The chiro gave me a sheet with some stretches. The ones that stretch my low back are these:
1. Lay on back, pull one knee up to chest with your hands under your knee. Do this stretch for 3 seconds, 5 times. Do other leg. Repeat another set.
2. Lay on back, pull both knees up to chest, bearhugging your knees with your arms. This one I can really feel the stretch good.
The sheet also has stretches for the adductors and hamstrings. He also suggested foam rolling my glutes. These last three are because I sit a lot.
Female, 5'3", 50, Max squat: 202.5lbs. Max deadlift: 225 x 3.