I've had some blood draws and and IV since getting RSD. I have RSD in all limbs,and hips. The only problem I had was with the IV. Luckily they had put it in as a precaution in the ER but it came out about half an hour after it went in. I was literally screaming in pain from that. With blood draws, no problems. It made my arm ache and hurt a bit more than normal for a few days but with no "good" arm, it turned out really well.

I wouldn't worry about getting your blood drawn.
Hugs,
Karen