You seem to have a needle phobia related to HIV, and we strongly suggest you seek counseling for that phobia.
NO MATTER WHAT, you aren't going to be infected by a needle unless you are sharing needles that are used to inject people with. Blood draws do not inject into you - they draw out of you.
Needlesticks are a very small concern. Despite the fact that many healthcare workers get needlesticks, and are exposed to fluids from HIV-infected individuals, only a handful of healthcare workers have been infected from occupational exposure to HIV, in the 40-year history of HIV.
Put this irrational phobia behind you, or seek professional help to overcome these persistent thoughts.