I don't generally have good news for customers who ask questions in the criminal law category, and this is one is no exception. No matter how old a felony is, whether it's violent or non-violent, or whether you served any time in jail at all, if you were convicted of a felony and the crime allows for you to be sentenced to more than a year of incarceration you lose your state and Federal gun rights.
Tennessee's policy's with regard to restoration of rights after a felony conviction are harsh, unfortunately. The only way to possibly restore your rights in Tennessee would be through a pardon from your governor.
Even that will not work to restore gun rights in all cases. An Opinion paper from the Tennessee Attorney General holds that even after a pardon, if your felony involved "the use or attempted use of force, violence, or a deadly weapon," or your conviction was for a felony drug arrest, a pardon would not be sufficient to restore your rights. Op. Att'y Gen. No. 84-063 (1984).
Nevertheless a pardon is useful whether or not it restores your gun rights, The application form is on the web. You don't need a lawyer to apply for one, so you have nothing to lose by going forward with this.
If you can get your offense pardoned and your gun rights restored in Tennessee, then the Federal government would lift the ban against your gun rights and you'd be able to own a weapon in Mississippi. But you must get your rights back in the state where they were taken away before you can own a weapon anywhere else in the country.