I'm sorry that happened to you.
I am usually pretty easy to get blood from, but I've had a couple bad sticks too - although not from Red Cross blood drives. This was for different blood tests.
I had one tech who wasn't even really watching what she was doing and after two tries of hitting nerves, I told her that I wanted to wait for the other technician. She seemed peeved and told me I'd have to sit a while and I told her that I was fine with that and I wasn't trying to offend her but I was in pain and wasn't going to get stuck again by her (for some reason, she refused to try my other arm too - so she wanted to go for try three in the already really painful arm). The other tech was great and very apologetic.
Most of the doctor's offices out here now send lab work out to be done and read so you have to get the order and go somewhere else to have it done...which almost always means ridiculously long waits (bring knitting!). Well, I went in one day and there were already 8 people ahead of me, three of which were basically planning how to rip the poor tech on duty to shreds when it came their turn since they'd been waiting for two plus hours. For some reason, their usual staff of 2-3 techs was down to this one poor guy who honestly WAS doing his best and was just swamped. The line moved slowly and when it came to the first of the two men who were complaining, he started yelling at the tech and the second man joined in - even SWEARING at him and calling him names! These were men in their 50s and 60s too (I always expect better behavior from that generation and am seriously disturbed when they act like jerks). Anyway, the poor tech was red-faced and apologizing and after listening for about thirty seconds, I'd had enough.
I told both of the men that none of us were thrilled about having to wait so long, but it wasn't this guy's fault that the place was understaffed that day and the guy was doing his best to do a good job with everyone. I told them calmly that it was totally unacceptable to talk to him that way and if they didn't stop, I'd call building security on both of them which would mean they'd both lose their place in line which I'd gladly take since I was way behind them. :-) They looked like they wanted to whack me, but thankfully, they shut up and sat down. The other people sitting there looked like they were waiting for the men to start in on me, but they just sat and pouted as only middle aged men can do.
How stupid is it to antagonize a person who is planning to draw blood from you anyway?! Sheesh!
The line went faster once these men shut their mouths and when the tech got to me, he thanked me and said he was tired because he hadn't had time for a lunch break. I had a granola bar in my purse and made him eat it and go get a drink of water BEFORE he drew blood from me. He was so appreciative. And he did a great job. After that visit, I wrote a letter to the company to praise this man but tell them how understaffed the office was and that they needed to either find more staff or start instituting appointments or something to prevent this from happening again. Who knows if anyone listens to stuff like that...but if it isn't said, I KNOW no one will hear so at least I tried.
That all being said, I'm sorry that happened to you...maybe you can complain about it. I'm sure those places are understaffed or perhaps not competently staffed at certain times.