Hola!
That's a tricky one. My CRPS started in my left knee, and I've had several episodes of spread since, over the last two and a half years. It's now throughout my left side, and in my right foot.
For me, each episode of spread has been a creeping in of symptoms gradually, usually starting with an ache and skin sensitivity, then with increasing pain. Although my knee and feet display a lot of visible symptoms, the spread in my other areas is different in character - and apparently this is very usual with areas of CRPS spread. The pain and allodynia can be just as bad, but i don't seem to get an many or as obvious signs of the colour and temperature changes.
I would say, first and foremost try not to panic. CRPS makes our pain centres overreact to any injury, and your IV counts as a small injury. It's important to keep your hand and arm moving normally, and obviously not to use ice. Try not to guard that arm, and to behave as normally as you can. Keep an eye on things. If it is spread, then the symptoms will happen more frequently and settle in. If it isn't, then things will normalise again.
In my own experience, I've had a couple of episodes where I've thought it was spreading to a new area, but then things have just quietened down and gone back to normal. It's important to remember that CRPS affects your nerves, and you can have some strange effects in any area of your body, that don't necessarily mean spread, just a localized area of nerve weirdness for a while.
Movement and normality are your best defence. And vitamin C every day! Sitting still and worrying about it would be the worst thing to do, and I'm sure you're not doing that, but I know how scary it is to think it is spreading
Good luck. Take care of yourself, eat well, and keep moving. Hopefully it will settle down. If it doesn't then let your CRPS doc know next time you see them. There's not much immediate that they can do IMHO, and from my experience, GPs or PCare docs can't do much more than note down new symptoms. My spread has been catalogued by my specialist, and although we've tried new meds, nothing has stopped or reversed the spread. Of course if you're really worried then ring your doc, if nothing else they might be able to reassure you.
Keep

whenever you can, it all helps.
Bram.