Any nurses? or experienced mothers that can help me

A❤
So I have a pretty bad needle phobia. Well I got my blood drawn at my doctors today for my first prenatal screening. I'm 24 yrs old and 6weeks pregnant. I had it done at my primary physician I know very well rather than my (new) obgyn. I took the order with me, and there was some confusion as to what exactly a "prenatal profile" included I guess the lab nurse needed more specifics. So she called and spoke with someone at my obgyn and got clarification. Took my blood as I laid down and when I sat up I almost passed out. The room was spinning! I'm already very lightheaded as it is from being pregnant. I also thought I was going to throw up but didn't. Well after some time i was ok and left. Well I just got a call hours later, that there was a mistake and they need to do ANOTHER DRAW. They need more blood. Can I refuse? I know the test won't be complete, but do some people completely skip it? Is it dangerous to not finish it?