How do I change a road bike into a commuter bike?
You can probably change the stem to something shorter with more rise and not have anything else to change. This may be enough to relieve the back pressure and the drop bars will give you more hand positions which I've always found easier on my carpal tunnel.

Changing the handle bars to flat bars will mean you have to get a set of shifters and brake levers to go with the new handle bar style.

I'd also recommend that you get a set of full wrap fenders so you can keep the road spray to a minimum.

I'm a designer and programmer so I understand the issues around sitting all day. A better investment may be in your chair at the office and your desk. You're spending way more time sitting there every day than you are on your bike. That is the place that you can most likely get the most benefit by setting it up for a proper ergonomic workspace.