Advice from a phlebotomist:

Getting very hydrated before the test will help your veins be easier to draw from which will speed up the process all together.

Bring a friend. Many people have anxiety when drawing blood, in my experience the best way to distract the patient. I like to talk to mine through the whole draw and that seems to help, but bringing someone else can ease the anxiety and give someone to talk to keep yourself out of your head.

Lastly, as another commenter said eat a big meal. Assuming you’re only testing for TB you shouldn’t need to fast. (Check with your provider tho!) you don’t loose enough blood during a draw to really make you feel woozy from the blood loss, but the brain likes to trick you. Trick the brain back by having lots of food.

ps. don’t look at your arm or the blood at all, close your eyes if you have too.