Welcome to Health Care Magic.
I have gone through your query and based on the information provided, the red line could be due to thrombophlebitis
of vein .
( thrombophobe) should help her. But it may cause rash
in few people. Please consult the doctor before using the ointment.Meanwhile hot water sponging or cold
pack of the area should help relieve her pain. If the IV line is still connected to the arm, then remove it and get the iv line secured to the other hand.
Hope you got the solution you were looking for.
Wishing your daughter a speedy recovery.