Just had my CD21 done. When I enter the exam room, the same dude who couldn't stick me at day 3 was there. This time even without a teacher. So I asked for someone more experienced. He responded with "oh, I think I recognize you" to which I showed my fist and told him "bruise this big, lasted over a week". He didn't say anything, but went to get one of the most senior phlebotomists they have.
She tried to give me grief for asking for her at first, but I responded with the same show of bruise size and then she said she understood.
Maybe in a few months, I'll let him stick me again, but not after he's truly had waaaaayyyyy more training.
Dude I don't blame you for wanting someone else to do it. You totally have the right to ask for someone else if the option is available. No one wants to be stuck more than once, or to be left with war wounds from a simple blood draw. Hopefully this time around was more pleasant!