If it was me, I would simply add some more iron to my diet and see if you feel better after a couple of weeks. It's not uncommon for pregnant mamas to be anemic. What are you eating/supplementing with now?
I'm a anemic right now and my m/w suggested that I take a tablespoon of liquid Chlorophyll and some alfalfa tablets to bring my level up. Other good sources of iron are Cream of Wheat, spinach, kale. If you go with the greens, try to have some vitamin C with it to help with absorption. You could make a spinach salad and add some citrus fruit.
That didn't answer your question, but there may be an over-the-counter test you can get at the pharmacy. Wouldn't hurt to give a call and find out.