Best way to fix that is strength training. Before I started strength training in my mid teens I used to get a sore back all the time but now I can sit for 18 hours slouched on a chair without a single pain because my lower back is really strong thanks to things like deadlifting and planks :-)
1-2x a week at the gym, 45-50 minutes of HIGHLY intensive weight lifting and you'll be sorted. More than twice a week isn't needed and if you're going as intense as you should be you won't manage the "3x a week" most gym-heads go unless you're roiding.
Intensive doesn't mean lifting weights too heavy, it just means you train hard enough that it hurts and you feel sore for days afterwards.
I go to the gym 1 day on, 3-4 days off. Easy and doesn't take up a lot of time. It's hard at first, but after 3 months it becomes easy and fun. Give it a go and you'll notice a big improvement in your working day. Things like carrying bags, taking out the trash becomes effortless too.