I'm going to answer the easiest question first. More likely than not, you do have Hashi's which is the most common cause of hypothyroidism. You were tested for only 1 out of the 3 different antibodies that can be seen in Hashi's (the other two being TGab (thyroglobulin antibody and TRab (thyrotropin receptor antibody). Please know that not everyone will test positive for any of the antibodies since biopsy is the only definitive method of diagnosis.
Bottom line, you are dealing with hypothyroidism and, based upon your labs, are not being medicated properly.
I don't know a single soul who would feel well with your below-mid-range FreeT4 level. Most people need their FreeT4 levels above mid-range and often closer to the high end of the range.
Inadequate FreeT4 levels can cause muscle/joint issues so, truly optimizing your FreeT4 level will tell you whether or not your thyroid is to blame for yours.
Since your FreeT3 level is proportionately lower in the range than your FreeT4 level, you are correct in thinking that you could benefit from the addition of T3 - either in the form of Cytomel or desiccated thyroid products such as Armour, Naturethroid, etc.
I know you mentioned in your other thread some issues in finding a thyroid-savvy doctor. Please know that Dr. Right is least likely to be an endo. "Whole body" doctors such as internists, DO's or alternative MD's usually "get thyroid" much better than endos.
You might want to try speaking to pharmacists (not the counter help) to get contact info for doctors that Rx Cytomel or Armour. There's no legal reason why they can't provide this information so, if the first one doesn't help, just move onto the next one.
Another idea would be to check the Top Thyroid Doctors site for a listing of doctors in your area.
Best of luck to you moving forward - please keep us posted!