I am not sure where you have RSD, but mine is in my right limb, hand to shoulder. I too am extremely sensitive to medications so I have had to find other ways to cope with the swelling.

1. One of the best techniques for me is to use compression on my arm if I have swelling. I grab a scrubbing brush or a towel and slowly scrub my kitchen counter back and forth in a rhythmic movement. This seems to really help hault the swelling most days.
2. I also elevate my arm (slightly) for short periods of time throughout the day. I alternate this with movement every 15 minutes in order to keep the limb warm and not so stiff.
3. I also use Epsom Salts baths quite a bit for inflammation when it gets bad. I fill up the sink using water that is 105 degrees and soak for about 10 minutes.
4. I will also drink a regular cup of coffee (I know, it sounds so wrong) but for some reason, it helps with swelling for me.
5. I also will get in a pool at a rehab center (it is warm water) and just slowly move about. I never notice the swelling gets better right after the water, but a few hours later, it really seems to kick in. I think the compression once again helps.

So these are my tricks I use and I use them daily because inflammation is a big problem for me. My fingers are always so swollen and stiff every morning. If it is bad, I start my day with an Espom Salts soak, this justs really helps sooth the arm and helps it move, which I think then helps with swelling for me.

Good luck to you. I hope some of these things will help.