E.B.
My daughter has had this test done many times (I am not a health professional). It was explained to me like this (I realize this is overly simple):
The ESR rate is commonly called a Sed Rate. When there is infection present, there are certain proteins that are formed that cause the red blood cells to clump together rather than flowing freely. Think caramel popcorn that sticks together in bunches as opposed to unflavored, unbuttered popcorn that is in single pieces. The lab technician observes how many red blood cells clump together by this sticky protein, and therefore sink to the bottom of a special test tube. If the protein isn't present, the red blood cells float around. If the protein is present, the red blood cells get stuck together and then they sink because they're in a clumpy mess. There can be a lot of the sticky protein and a lot of clumped red cells (resulting in a higher number) or not a lot (a lower number). The antibiotic doesn't affect the test from what I have been told - it's all about the infection.
It's a way for a medical professional to tell if there's inflammation present - due to infection, or a multitude of medical conditions. If your daughter has a pretty significant infection, the Sed Rate would be high. The test may be repeated (and probably should be) and there may be additional tests (just blood tests at first). The Sed Rate should come down after the infection and resulting inflammation clear up.
Make sure your daughter's doctor re-tests her Sed Rate after a reasonable amount of time (usually a couple of weeks, from my experience). Ask your doctor when the Sed Rate test will be repeated.
Apologies to the nurses and doctors on here if this explanation is completely screwed up - I'm willing to be corrected. Just was trying to help.