is it normal to feel sore in the arms after getting blood drawn?

Yesterday, I got my blood drawn, they took about three tubes of blood. And during the night to the next day, I have been feeling so sore in my arm and sometimes a bit numbness but the funny thing is, I got blood drawn from my left arm and my right arm is the one that is hurting at the moment. I did take birth control that made me have severe side effects and I did sleep on right side the whole night, so maybe that is what is causing the numbness and soreness.

When I woke up, some of my veins in my fingers were also purple. Should I be really concern about this?