hello, your daughter suffering from superficial thrombophlebitis due to i/v drugs used especially repeatedly at same area it is a condition in which due to damage of vein wall due to injection a thrombus is formed at damage area which may get infected as you say overlying skin is red and swollen and hot to touch it is the sign of inflammation or infection . usually treatment is avoid repeated injection at same site , if swelling is marked elevated the affected limb by putting pillow under the arm and forearm and should be above the level of heart so swelling decrease , local application of heparin gel over the thrombosed vein, take anti inflammatory drug which contain serratiopeptidase , and a antiboitic dose according to weight.