It's impossible to know what's going on without the Free T4 test. Some medications can affect conversion, but without enough Free T4, there's nothing to convert.
I'm not sure where you got the information about metoprolol and gabapentin. If you have a link to the article(s), I'd like to see them because that's new information for me. I was on gabapentin for quite some time (years) and none of my doctors ever worried about conversion, nor did I have a problem with it, other than my usual conversion issue for which I take T3 medication. We did not have to adjust my dosages to accommodate the gabapentin. Of course, we're all different. I'd look forward to seeing those articles or knowing where you found them.
You can always discuss this with your doctor.
Was there a Free T4 test ordered as well? If so, what was the result?
With Free T3 as low as yours, we'd expect TSH to be higher than yours. Since it's so low, I'd suspect that you might have Central or Secondary hypothyroidism. With Secondary hypothyroidism, the thyroid actually works fine, but there's a problem with the pituitary gland in which it doesn't produce enough TSH to stimulate the thyroid to produce enough thyroid hormones. It's still hypothyroidism and has to be treated with replacement hormones.
Hopefully, she will get you started on medication as soon as possible. Since this is possibly a pituitary issue, it would be a good idea to have other pituitary hormones tested as well in case other imbalances could be contributing to your symptoms.
Excerpt from Best Practice - Thyroid Function Testing:
"Normal TSH - associated with a low FT4 and/or FT3
These results may occur following secondary (central) hypothyroidism, which is associated with pituitary or hypothalamic dysfunction. TSH can be low, normal, or slightly elevated. Evaluation for deficiencies in other pituitary hormones should be obtained before imaging (i.e., pituitary MRI). Hormone tests should include: ACTH with cortisol, FSH, LH, oestradiol (female), testosterone (male), prolactin, GH, and (insulin-like growth factor 1 (IGF1). For this condition, thyroid replacement therapy is monitored by checking the levels of FT4 and FT3. [23]
Other causes include drug use (e.g., phenytoin, rifampicin [rifampin], carbamazepine, barbiturates) and assay error when interfering substances are present."