There's always discrepancy about what's normal and what's considered Graves Disease.
I do see that your doctor tested TPOab, but apparently, didn't test TgAb to completely rule out Hashimoto's. There are people who have hypothyroidism in early stages of Hashimoto's, plus there are those that have, both, Hashimoto's and Graves at the same time.
According to your Free T4 and Free T3, you clearly have hyperthyroidism, so whether your doctor will diagnose Graves or not, you need treatment.
Why can't you take medication? There is no natural way to treat this, though some say you can help it by altering your diet.