When a patient is given the "normal" discussion on thyroid levels with their doctor - usually that is there way of shutting the door in tweeking treatments.
I am not saying you are not normal in ranges - but if you are still experiencing symptoms of hair loss and other hypothyroid symptoms - to me - it is obvious you are NOT normal.
Everyone has antibodies - non thyroid related and thyroid related individuals - when they start attacking - then there is an issue. I have seem many people here post TPO antibodies in much higher levels than yours - so I am not sure if those are really causing the problem for you.
You mention T3 T4 levels. If it is the standard "inbound" T3 T4 levels you are being tested for those is useless.
You need the Free T3 and Free T4 test to determine where you are with your condition.
If your issues are hair loss with no other symptoms - I am going to assume your FREE (see that word FREE) Free T3 levels are not correct for you right now and must be tweeked to rid the hair loss.
Many hypothyroid patients experience a symptom free life when the level of FREE T3 are on the higher end of the "scale" and of course then the TSH value drops.
You may get relief finding your TSH number for your around a .5 - 1.5 to help you.
They type of thyroid antibodies test is the key to what the high levels might mean. There's a few sites out on the net that will describe each of the tests and what they are for. I had normal TSH, T3/T4 levels with a high Thyroglobulin level which lead to my thyroid cancer diagnosis. But, from the info I have read on the net, you can be perfectly healthy and still have elevated thyroid antibody levels. I'd just see which test it is, and ask your doc for more info and what he/she is looking for the test to indicate. BTW, I notice you mentioned internist. I sometimes have my pcp do my bloodwork, but because of my history, my endo alwasy determines dosage, etc. If you are not seeing an endocronologist at least periodially, I personally would recommend it. I would be suspect that your levels are correct since you are experiencing hair loss.