It only took me about 15 years to get diagnosed so you're not alone.
Your FT4 is very low. You should be in the top third of range and you are now at the bottom. I'm sure a Free T3 would confirm that you are hypoT.
You need to tell your doctor that you believe you are hypothyroid based on the list of symptoms you have. Then request that he draw a Free T3 and the antibody tests, TPO-Ab and TG-Ab. You will need a vitamin D and B12 level done as well as ferritin. If he refuses to cooperate then your only choice is to find a doctor who knows how to diagnose and treat you... or continue to be miserable until your TSH finally creeps up to "out of range". Mine never did so it might be a long wait indeed.