Can you get a blood test to determine if you have enough iodine in your system?
No, there is no common test to determine how much iodine you have in your body. The American Thyroid Association discusses this in their article Iodine Deficiency.
I added a link to that article from the Iodine page on VeganHealth.org.
If you have no idea if you get enough iodine, please check out the links!