Blood work for 9 month old?

I took my baby to his 9 month check up today and they wanted to do blood work to check for anemia and lead. Well when they tried to take blood the first attempt she blew a vein in his arm so they tried on the other side and couldn’t get it. They held him so tight he was red he was screaming and crying like I’ve never seen him cry before and all for nothing since they didn’t get blood!! Is this normal??? Do they usual get blood this early?? Do they usually use the arm??? Do they really need that much??? I have a daughter who is 9 and had a lot of health issues. They took ALOT of blood when she was a baby and never like this. From what I remember they used her foot or ankle or leg or something. He get told me to bring him back so they can try again but I really don’t want to! Advise help please!!!