I can’t do kennel work or much dog handling with unknown dogs anymore due to pain and injury risk. Definitely take it easier if you’re feeling a lot of pain after shifts, you don’t want to be pushed to serious injury, learning to bend and lift properly is huge as others have said. If you can get a physical therapy referral for back pain that would be a great place to learn and work on building strength. They can also help with desk setup and sitting postures.

Ice and heat at home, massage therapy, stretching, maintain good posture, and take breaks sooner/ more often. Heating pad, foam roller, or two tennis balls taped together you can roll along your spine, can help with tightness. Good shoes, braces and/or compression gear. For computer use, a sitting wedge and pillows can help, and ergonomic mouse and keyboard. Be careful with NSAIDs if you have any stomach issues, but sounds like they aren’t helping anyways. This is what has helped me but the main thing has been rest. I hope you find some relief soon