The lump you had was probably a hematoma (blood clot under the skin and around the vein that was used to insert the IV). It is fairly normal and common to have this occur because as the needle punctures the vein wall and stays inserted, your body's natural response is to form a clot around it to stop the subcutaneous bleed and close up the wound to prevent further blood loss. It will bleed again when the IV needle is removed and again, your body forms a clot to stop the bleed. Thus leading to a lump.
The pain and tenderness is from phlebitis, or inflammation from the insertion site and the act of inserting and removing the needle. Your hand has very little fatty tissue and is easily irritated from minor trauma such as this. It is further aggravated as they connect and disconnect several times to exchange IV fluids, medication, antibiotics, etc.
To help with the pain, you can treat with a simple anti-inflammitory such as Ibuprofen. If it doesn't go away, gets worse, becomes warm to the touch, or increasingly more red, seek medical attention. You may have developed an infection at the infusion site (IV site).
Hope this helps!