Here we can appeal in person or mail it in, don't know how it's done in Tennessee. This happened to my Mother quite a few years ago and she fought back. If you still feel confident, submit the photos along with a very well written request for reassessment. Since you recently purchased the home, I would make a guess that your city has looked mostly at the sales price of the home in re-assessing your taxes. This comes as a surprise to many new home buyers.
Many places are very slow to re-assess a property, and they have limited resources to do so.
When the home sells, they have the public records from the sale which give them a good idea of the homes new value, and the tax bill goes up. This can be an unexpected whammy, but it happens a lot. It Could Go Up Jim needs to keep in mind that once he appeals the tax appraisal that it can go either way. Come to find out, they had appraised our neighbors house as ours. When he started talking about brick and a full basement, I knew he had the wrong house.