i find that the more weight i can put on my hands, the better my back feels. a lot of people think that a more upright riding position is good for the back, but for me, just the opposite is true. i also ride with a backpack (but no heavy laptop or locks, just clothes, cell phone & wallet) because i like having the weight on me instead of the bike, but in your case, you might want to seriously consider going back to a rack and panniers if you absolutely have to lug around a laptop and heavy locks with you.
i would suggest ditching the laptop if you can and just carry a small flash drive with any necessary files and documents you need to transport between your home and office computers.
and yes, go to a doctor before the problem gets worse.