My total WBC and neutrophils are high and rising. What kind of diagnostic avenues should I look at?

High WBC Count. An elevated white count can be benign such as from use of a steroid medication, moderate concern as with an active infection or high concern as with a developing hematologic disorder like leukemia. Reviewing medications, looking for infectious sources such as endocarditis is important. Lastly, a consultation with a hematologist is required for a probable bone marrow biopsy to assess for a cancer.
Work up. If your WBC and neutrophils are rising, then someone ordered those tests and he/she needs to have a work up in mind if those are elevated. Usually, elevated WBC and neutrophil counts indicate infection, provided the rest of the differential is normal. There are some blood disorders that are manifested with wbc/neutrophil elevation. Steroid hormones may cause elevation of the same.
See below... You may have an infection or an inflammatory state even in the absence of symptoms. If you do have some symptoms, i recommend repeating the CBC to make sure values are returning to normal; however, other explanations are possible including serious diseases like leukemia, more specifically chronic myelogenous leukemia. Please consult your doctor or a hematologist.