If I have a low iron count, what tests should be done to figure out the cause? Dietary intake should have been sufficient (lots of meat and greens)

Whoa. I'm going to assume that someone is not using the term "iron count" as a synonym for hemoglobin / hematocrit, but that you have an actual low measured serum iron and high iron binding capacity. If not, other causes of anemia must be sought. If you do, check for GI blood loss unless your monthly loss is very heavy. Contrary to "pop" disinformation, greens aren't a source of iron. Glad UR proactive.