Hi Hannah! I'm sorry to hear about your new health challenges, but it sounds like you're staying optimistic about transitioning out of the military. I got out of the Army about 2 years ago and it has been an exciting adventure.
So full disclosure, I don't own any rentals in the East TN area (yet), but I was born and raised in Knoxville, so I may be able to help a little. There are several great markets in Tennessee, including Knoxville and it's surrounding suburbs. West Knoxville, particularly Farragut, is a higher priced area with more commercial growth. You'll find more A class neighborhoods there than anywhere else. Karns, Powell, and Halls are great communities in the north with steady growth and decent schools. As you get inside the 640 bypass closer to downtown, you'll find less B and more C/D class residential areas mixed in with the commercial areas. In the downtown area, there are a lot of people buying fixer uppers to rent to the college students that go to UTK. If you're planning on BRRRR'ing most of your houses, it might not be a bad idea to start looking away from the college. UTK is a pretty big party school, which eventually means trashed rentals.
Another area to take a look at is Maryville. It's been a growing area for awhile now, but since it's still outside Knoxville, the prices may be cheaper. There are several large business around Maryville, so you should find a decent customer base.
Hope you find some great deals down in Knox-vegas and feel free to ask more about the area.