Since there is associated neutropenia or low neutrophils, it is more likely to be due to Vit B12 or folate deficiency.
Blood cancers result in very low or very high
blood cell count. This is not yet evident in your case. While you wait to see a specialist, get a peripheral smear to see the cell types in your blood. Also, start eating healthy and ask your doctor if you can start vitamin B12, folate and iron supplements. Take care!