The problem you are facing has developed because of the injury
to the wall of your vien while drawing the blood.
The vein becomes irritated and injured because of wrong drwing technique, faulty material of the drawing needle and sensitivity of body to such a material. This is called Thromboflebitis.
You need to apply locally available cream to treat the situation (ask your chemist for a Heparin
Avoid drawing blood from the same area again and keep the elbow at rest as more movement would further increase the inflammation.
Consult your doctor if situation worsens or persists beyond one more week.