When you have blood taken for a test, the tube pulls your blood out of your body. It is not able because it's not designed to push any blood back inside your body. Therefore, your concern is totally illogical and would never happen in reality.
I don't think anything I say will convince you that a professional phlebotomist would never use a dirty needle.......so I think your only choice is to retest. Tell the phlebotomist that you want to watch EVERY step of the process from putting on his/her gloves, opening a new syringe directly in front of you, inspecting the collection tubes to assure they are clean......everything.
The vast majority of phlebotomist understand that SOME people have real fears about sharps and tubes being contaminated and are very accommodating in easing your fears.
Make sure you are well hydrated before you go for your retest. Perhaps you could even bring your own bottle of water in case you need to drink some more and the phlebotomist will not have to leave the room.
If you do all these things, you will be 100% sure the procedure was done with new and sterile equipment and will be able to relax and trust that your results will be accurate.
I wish you the best
A professional phlebotomist would NEVER, EVER reuse a needle.
We don't play "what if" games here.