What is the significance of the ointment gift from Haymitch in The Hunger Games?

At this point in the plot, Katniss has been trapped in a tree by the Careers with a tracker jacker nest over her head. She has been badly burned and does not have much hope of escape or survival in her precarious situation. During the anthem, Katniss tries to saw the limb which holds the tracker jacker nest but doesn't quite finish before the anthem's conclusion. She slides back to her fork in the tree when she finds a gift: the ointment.
This is significant because it gives her hope in a couple of ways. First, she had begun to feel that Haymitch had given up on her. Now she is certain that he is outside the arena fighting for her and with her, securing gifts on her behalf. Second, it provides insight that she has a base of support outside the arena. This ointment is almost miraculous; it heals injuries on contact almost immediately. When Katniss rubs it on her wounds, it "transform[s] all the angry red patches to a soft baby-skin pink" and helps her leg wound as well, though that one takes a bit more medicine because it burned deeper.
Katniss realizes the extreme cost of such medicine and knows that "many sponsors have contributed to buy this one tiny pot." Since it provides her the physical ability to continue in the games, it is "priceless" to Katniss.