I haven't been to any of the listed places that require a Yellow fever vaccination. So do I need to show proof of visiting a travel clinic to apply for my visa? The website of the Chicago consulate wasn't clear.
No. As long as you haven't been in one of the "Yellow fever countries" within the last 90 days, you don't have to get any vaccines. Although, if you're traveling to an area of risk, like the Amazon, it would definitely be recommended.