Yes they are the same, if you have them then you will have them for life, neither NT nor Levothyroxine get rid of the antibodies, but just treats the hypo that comes as a result of the Hashimoto's .
Do you know what was your TSH prior to starting NT ? for how long did you took it ?
The symptoms that you mentioned above are indicative of being hypERthyroid, it can cause under weight, rapid heart beat, anxiety and much more.
It is very possible that you do not need any thyroid hormone replacement and either that you do/did not have hypo, or that it was a transient hypo.
You can repeat the TSH, FREE T3 and FREE T4 in six to eight weeks since stopping the NT and to go from there!
The specialist who treats hypo/hyper is called Endocrinologist, you can ask your PCP to consult with one !
p.s. Do you know what are the reference ranges for the FREE T3/4 tests that you posted above ?
Best of luck,