Indiana will amend a birth certificate with a court order. The court order does not have to originate in Indiana. You could petition a court in Illinois, get a court order for the change, and submit that.
Depending on where you are in your transition, you may need a court order to update your driver's license in Illinois. If so, the same court order could also be used to amend your birth certificate in Indiana.
I would also advise getting a Passport. The passport demonstrates both identity and citizenship, so it can take the place of both a driver's license and birth certificate for those purposes. If you weren't able to get the birth certificate amended, you could just substitute the passport in any situation you might've needed the birth certificate.
Tennessee would not be informed that you had previously updated your documentation. When you go to the DMV to get a Tennessee license, you would be handing in your Illinois license which says you are female and they will be none the wiser.
Depending on where you are in Illinois, see if there are any trans advocacy or support groups around you that could advise on the court order. The clinic that does my hormones offers free legal sessions once a quarter where people get help from lawyers on all the name/gender change documents and court orders. If you're near a larger city, I'd be surprised if they didn't have something similar there.