If you actually saw dried blood in something, why didn't you point it out?
At no point in the blood drawing process should blood get on the needle holder. I'm not sure what you saw, but it wasn't blood.
If, by some weird chance it was, it was dried, and couldn't get into the tube that held your blood to impact your test result. Nor could it get into your arm.
This is an irrational fear.
If you are ever getting your blood drawn, or having any medical procedure, and are uncomfortable with something, you are allowed to stop and ask questions.
If this level of anxiety is normal for you, you should talk to your doctor about it.