Having suffered severe sciatica to the point where I could only sleep on the floor and started dragging a foot, I can attest to Peter M's main point: get your spine moving.
Cobra pose is also a really good one for this problem. You can actually read and work on a laptop while on the floor in a similar position using your elbows to support your upper body.
The key is to stretch the lower spine backwards and open the spaces between the vertebrae. Curving forward squeezes the discs in the lower spine and can push them out of place and put pressure on nerves. One big mistake I was making was trying to do stretches where I leaned forward attempting to touch my toes without keeping the lower back flat. This can greatly exacerbate the problem.
The next step is to improve strength in your transverse abdominal muscle. If you are like me, you were never taught about the existence of these really important muscles. As far as I knew, 'the abs' were the 'six-pack' vanity muscles in the front which you work by doing crunches. The transverse abdominal muscles are far more important. When tight, they hold your guts in and can help take pressure off of your spine.
Imagine a basic round balloon that has a string inside of it that's attached at the top to the tied end from the the top running through the middle. When you squeeze the balloon, it lengthens and the string will be pulled taut. Here's an extremely professional diagram:
When you tighten your transverse abdominal muscles, your abdomen is like the balloon and your spine is like the string. In this way, you can relieve pressure on the spine while sitting and standing. This is sometimes called "holding your 'stomach' in" and for some reason there's a negative connotation to doing this. Hold your 'stomach' in as much as possible: your back will thank you. It also has the benefit of making your actual stomach smaller which helps reduce appetite and overeating.
There are various ways to strengthen the transverse abdominal muscles. Planks are my preference. There are lots of ways to do these just getting into a push up position and holding it is a good start. Crunches and sit-ups will not help at all with this and I would avoid doing these at all if you have back pain.
Pain in the shoulders often (unintuitively) originates from the chest. The problem is that we sit with our shoulders forward all the time. We typically don't exercise the complex set of muscles that pull the shoulders back. We then end up with weak back muscles trying to fight against strong chest muscles. If you do push-ups or other chest-strengthening exercises, you need to also train your back muscles such as with pulls.
A good stretch for relief is to stand is a doorway with your palms on the frame. Lean in gently until you feel a stretch in your chest. Try different arm positions as there are various muscles in the chest. Swinging the arms backwards to attempt to clap the hands behind the back is a nice active stretch (check the space around you.)
Good luck in your studies and resolving this problem. I hope this advice helps.