Posture Brace

I'm not sure a posture brace will help.
You need to look at your work station, your chair (does it have arms, is it the right height for your desk, does it have lumbar support, etc), the height of your monitor (I use to put mine up on a few reams of paper to get mine at a good level).
I slump less if my monitor is at or slightly above my eye level.
I find my wrists ache horribly if my chair arms are not about level with my desk.
Also - even the most comfortable ergonomic work station in the world was never designed to sit at for hours non stop from morning till night.
You need to stand up and stretch every so often - the recommendations I've seen is every hour.
You can do neck and shoulder rolls to help ease the kinks out.
A short walk about (get coffee, visit rest room, etc) should help relax stiff muscles.
Consider taking a yoga class so you know how to stretch and to help with your posture.

Have you had an ergonomic evaluation done for your workspace/computer desk? I would start there :)

I would suggest seeing a personal trainer who specializes in functional fitness. There are a lot of small muscles in the back and around the shoulders that don't get exercised in the typical workout and they get very weak.

Yes to an ergonomic evaluation. You might be sitting at a poorly designed work area. Also, see if you can get a few visits with a PT or a yoga therapist. In my opinion, it is better for you to have your body learn to do the muscular work to undo bad posture. If you become reliant on a brace, then your muscles still won't be trained to hold yourself up the correct way.
I teach yoga and we work on this "spinal alignment" ability a LOT in classes.

Next: is there any way you can reduce the # of hours at a computer to less than 60?

Sounds like something I went through about a month ago from sewing. I ended up getting a brace and it was almost as bad as the pain I was in. I would say that it didn't help and, it chaffed me even through a shirt. I got a large pilates ball and have been using it for my chair at the computer and that has helped greatly. I also haven't sewn much because that seems to trigger my pain. I discovered that I had my sewing machine too high and my chair to low. I'm looking into an ergonomic sewing chair so that maybe I can sew without pain. I also had a massage and that helped me tremendously, but not every massage therapist knows what to do for this kind of pain. A few years ago, I experienced the same thing and saw a chiropractor. He said the x-rays revealed some degenerative change. Chiropractic care helped initially, but then hit a plateau. I ended up in PT and that helped tremendously and I didn't have problems until I started doing marathon sewing. It's the foreward head posture of sewing that really seems to aggrivate my neck and shoulders. A friend who has severe neck problems even following surgery, recommends a book on Egoscue and swears that by following the exercises he is pain free. If he gets lazy and lays off the exercises, the pain returns. It's at least another avenue to look into. Don't waste your time or money on a brace. I went with a hightly rated one and was really disappointed. Hope you get better soon, I really can empathize.

I haven't read other posts yet, but sitting on one of those body balls at your desk instead of a chair really helps with posture and keeping your shoulders back. A coworker sits on one and my previous doctor sat on one.
Make sure you get the right size though for desk height. Good luck

I'm with the others in thinking that a posture brace isn't going to work for you. It will not correct anything since you are finished growing.

In addition to making your work station better I think you really need to strengthen the muscles in your back by working out with exercises specifically targeted to those areas in your back. Once those muscles are stronger they will lift your posture. While sitting at your desk it is important to really be aware of your posture. Maybe stick a post it note on your monitor that says, "are you sitting up straight with your shoulders back?"

As for the exercises, you could keep some weights under your desk and even use them at your desk during breaks. Your chair can be your "weight bench" and even the edge of your desk can give you something to hold onto.

Hope this helps! I had scoliosis when I was younger and had to wear a brace.....so my posture is always something I have to deal with as well.