(THIS IS NOT OFFICIAL MEDICAL ADVICE.)
It’s definitely not pointless.
Normal free T4 goes up to 11ish (labs vary) and yours is 13.4. Your TSH is normal range at both 2.12 and 2.57, but if your free T4 is high and you have other symptoms, then something is still going on (I assume you had these tests because you have other symptoms).
Your free T4 is your pituitary gland sending signals to your thyroid. If your thyroid was functioning normally, this number would be normal. But as it isn’t, it means that somehow your thyroid isn’t getting the message to make the right amount of hormones, so your T4 is the pituitary gland sending more and more messages. (At least, this is how it’s always been explained to me). So, your symptoms should include, at bare minimum, exhaustion probably?
Some conditions with high free T4 include thyroiditis, consuming too much iodine, and Graves’ disease. Maybe check the symptoms for thyroiditis and Graves’ disease and see if either line up with any other symptoms you have?
If you were suspecting hypothyroidism (commonly what thyroid tests are for), though, it is most likely not that as it would cause low free T4. However, I know it can be confusing as both too much or too little can cause exhaustion and feelings of unwellness.
Good luck, as I’m sure this is frustrating so have these
and I hope you feel better soon.