1/ Sed rates, aka ESR, do fluctuate, as a variable response to inflammation in some people. Usually, inflammation causes the serum of the blood to "thicken" ( actually become more viscous) which causes slowing of the settling rate of cells through it, which is what Sed rate measures...the rate of erythrocyte (red blood cell) sedimentation (settling). It can climb quite quickly, but sometimes takes a long time to return to pre-inflammation levels, so is not terribly accurate for acute inflammation.
2/ Sed rate and C-reactive Protein both measure inflammation, but in different ways. The ESR is more indirect, but the CRP actually measures proteins produced by the cells when they are inflammed, and so is more direct, and reacts more quickly to changes in the inflammation.
3/Anti-inflammatories will, over time, reduce the Sed Rate, but only if no more inflammation develops. For proper interpretation of the test, however, your doctor should be aware of everything you take, including some seemingly unrelated things like blood thinners and supplements that can cause blood thinning, since they would have an influence on the viscosity of the serum and change the results.
As for me...I haven't had a normal ESR in 35 years! For the first 25-28 of those years, it was consistently over 100, often over 150. Not until I started taking Prednisone, Methotrexate and Plaquenil, 8 years ago, did it start to drop, and my last one a month ago was 34! Oddly enough, I don't find any less discomfort when it's lower, although a nurse once said (when she saw the ESR of 130)...that's gotta hurt! Personally I don't think it's a direct ratio.