Is It Normal To Feel Dizziness, Fainting, And Left-side Weakness And Arm Pain After A Blood Draw?

Hello. Today morning i went to have a blood prelevement in the laboratory and after taking the needle out of my skin, i started feeling dizzy and passed out (still feeling dizzy)and Well the problem is that my left arm (the arm used for blood) hurts i feel feel pressure in there in the whole arm i cant actually move it or lift anything, i can only do some slow movements or it will hurt if i dont . Well after a moment i started feeling pressure on my left arm too and my left back . My whole left body part feels weak. Is that a normal reaction ?