I have a similar situation with my 6 year old daughter. She has anxieties about so many things, and pain is definitely one of them. She has had splinters too and refuses to even let us look at them. What we've done for that, is had the "Tooth Fairy" take them out for her. During the day she worries about EVERYTHING, but at night, she seems to be a good sleeper. We waited until she fell asleep and then with a flashlight and tweezers, we took out her sliver (we've done this twice now). She slept through the whole thing. She did fidget once or twice, but slept through it all.
As for the shots, we just did that too, we thought we were done until she was 9 or so, but she had to have a booster. When she found out, she started crying in the middle of the apt and really didn't stop until we were done. When the shot was about to happen, she was screaming. I did hold her tight and hugged her hard (to keep her hands from moving) and they did it in her leg. It was hard, but short. I just try to really explain that shots are good for you, and the pain is short. That if we didn't get the shots, she could get sick and the pain would be longer and worse than a short shot. The doctor also suggested she try chanting, "I'm braver than I thought, I'm braver than I thought" and that by the time she got through that a few times the shot would be over. I tried, "I think I can, I think I can" or other mottos. She still cried and screamed, but at least it made me feel as if I was doing something to help
If your daughter is going to go to kindergarten, I know the schools also want you to be up to date on your immunizations, so ask before postponing. It's definitely hard to have your child so afraid and crying, but I feel that this is a case where you have to work through it as best as you can. Maybe talk with the doctor about her reactions (almost fainting, etc.) so they can best help you as well.
Good luck from someone who has a "worried" daughter too.