She probably has strep systemically, as she was not treated with abx. For the confirmed strep in January. Then she was simply on ammox., not enough to wipe out strep that she's had for months. My daughter had strep for 6 mos. that would not respond to abx. During that time she developed pandas. It took a big gun abx....clindamycin, to finally eradicate it. She too did not rise titers...it signals an immune response problem. If she did not test positive on the culture, but did so on rapid, its likely that it wasn't a good swab/ sample.
Best advice....see a PANDAS doc. Have her swabbed for strep, even if you take her to a walk in for documentation purposes. This may get her a stronger rx. Also, strep lies in places other than the throat, so that may be a possibility as well since she's had it a while.