Low T4 high TSH is the normal case, where Thyroid is not functioning properly, and possibly it is being damaged due to autoimmunity. This is Hashimoto's Thyroiditis in 90% of the cases. So it is important to get tested for Anti-TPO, to determine whether there has been ever Autoimmune activity. This number cannot be easily reduced. The other test is Anti-Thyroglubulin or Anti-Tg. This number is high during an active attack. The other most probable case is Iodine deficiency, which is not very common. In these cases it is helpful to take Thyroxine (aka T4) medication.
Low T3, with normal T4 is the problematic case. Because in this case it is likely that there is a chronic condition in the body. To avoid stimulating the condition, the body has reduced T3. In this case we should find and eliminate the underlying problem. Because just adding T4 or T3 would likely cause the issues that the body is trying to prevent.
Low T3 can also be possible due to damage of Pituitary gland, due to an autoimmune issues.
One case which seems to be helped by T3 (cytomel) is when the body temperature is also low along with Low T4 and low T3. This doesn't seem to be very common though. If you happen to have low body temperature then measuring it and adding T4 and maybe T3 to get the body temperature might be possible. But we don't know what side effects this would cause.