Yeah, it sounds to me like a definite Yeast infection and probably a Bacterial infection as well in her GI Tract...By the way, NEVER allow any Vet to give you ANYTHING to give your bird in her drinking water! I'm actually quite shocked that a CAV would ever prescribe that route of administration in the first place, usually that is done by Exotics Vet. The problem is that two-fold, #1 You have no way of knowing how much of the medication/supplement/vitamin or whatever it is you're putting in their water that they are getting, so they either don't get an adequate dose (this is what usually happens, as with your bird), OR they overdose and become very sick or die; and then #2 Their drinking water becomes immediately contaminated and starts growing Fungi and Bacteria! It's very unsafe and totally ineffective...Always give them oral medications, supplements, vitamins, and anything else directly into their mouth/beak.
***I also highly recommend that you go to any Petco and buy a bottle of Qwiko Avian Probiotics, or any Tractor Supply and buy Benebac Probiotics, and start giving your bird a daily dose starting immediately, and continue it every day for at least a week AFTER she finishes the Antibiotic. I have been giving all of my guys a daily dose of the powdered Qwiko Avian Probiotic every day for years, and they've never once had either a Fungal or Bacterial GI infection. I also take one every morning with my multi-vitamin. Any time anyone takes an Antibiotic, it can kill-off the healthy, normal, "good" Bacteria that lives throughout their GI Tract, which is the only thing that keeps Yeast from growing throughout their GI Tract, and this is the main reason they develop GI Fungal/Yeast infections. A bottle of Qwiko Avian Probioitics only costs $10 and it lasts forever, it comes with a pre-measured little tiny scoop, and all you do is put a scoop-full every morning mixed into either their pellets or their seed-mix. That's it. Again, continue it for at least a week AFTER she finishes the Antibiotic so that all of the healthy, normal Bacteria in her GI Tract is replaced...
***Watch her carefully, and if she has not COMPLETELY STOPPED picking around her vent/tail area by the time she finishes the Antibiotic and the Anti-Fungal, then you need to IMMEDIATELY call your CAV and make an appointment for an X-Ray right away...I wish I had the link to the post written by our other senior member and their Amazon, but I was actually shocked that their CAV caught that Kidney infection on the first appointment by doing an X-Ray, and I was even more shocked about the damage that had already been done to the bird's Kidney and mostly his Spine.
That bird's ONLY symptom, the only one, was their picking around their vent, and it wasn't even being done every day or even every week!!! This senior member had seen their Amazon picking around their vent once in a while for months, but it was so infrequent and because the bird was totally fine otherwise that they thought nothing of it until it had gone on for months and months...And you know how birds are, they hide all outward signs and symptoms of illness for as long as they can...So this bird had hidden all signs of pain, illness, etc. except for a very occasional plucking/itching around his vent...And after months of seeing their bird do this infrequently, this member posted about it here, and I believe I and others told her that it may be a GI Tract infection or some kind of feather-follicle that was infected...She took him to her CAV and they ran a Fecal Culture, blood work, and an X-Ray, just because they wanted to cover all the bases...The blood-work showed nothing but elevated White Blood Cells, and the Fecal didn't show anything I don't think...But that X-Ray!!! I have never seen anything like it, and I have no idea how that Amazon was still eating, moving around and flying normally, and not acting like they were in any pain at all except for that plucking/itching around their vent!!! His right Kidney was SOOOOOO LARGE that it looked like it was ready to burst, literally...And it was so enlarged from the infection that it had been putting pressure on the bird's spine for months, and this causes severe degeneration of his spine in the area the enlarged kidney was pushing on, and you could clearly see that his spine had started to break-down right in that area!
It was such an odd, freak thing that was hidden so well by the bird that there was no bird owner in the world that would have suspected that their bird was at all sick, let alone sick with a potentially fatal infection and spinal-damage because of it. Unfortunately, most bird owners would not have even taken their bird to the Vet in the first-place, as this Amazon wasn't even plucking/itching his vent area even as much as your Love Bird has been, so there is no way that only that would tell most people that something was wrong with their bird (after all, they preen daily anyway)...And what's more impressive is this member's CAV!!! I remember being so very impressed that this CAV took an X-Ray on this bird's first appointment, because I would be willing to be that only 10-20% of all CAVs, probably less than that, even the best in the world, would EVER think to take an X-Ray because a bird present "occasionally plucking/itching the area around their vent a few times a month" with no other signs or symptoms. Most would run blood-work and a Fecal Culture/Gram-Stain, and when the White Blood Cells were elevated and the Fecal showed Bacteria/Fungi, they would have diagnosed the bird with a GI Tract infection and given the appropriate med for it, and that would be it...and the bird would likely suddenly crash at some point all at once and in a lot of cases die suddenly and without warning...So that CAV quite literally saved that bird's life and also saved his spine from becoming permanently damaged and the bird disabled...
***So, my point to this whole rambling post is that If your bird finishes the entire round of both the Antibiotic and the Anti-Fungal meds and she is still plucking/itching around her vent/tail/leg areas, please call your CAV immediately, like the day she finishes the meds, and take her back demanding a regular X-Ray! I'm not trying to be an alarmist, but after seeing that entire episode with that member's Amazon and the total lack of any other signs/symptoms, and then seeing that X-Ray, you can bet that if any of my birds EVER start plucking/itching continuously around their vent/tail area they are getting an X-Ray done immediately!!!
If I can find that thread I'll post a link to it here, because it's an interesting read as it matches-up exactly with what your bird has been doing, and the diagnosis was so unexpected...and that X-Ray is something to see, it really showed me just how well birds really do hide all outward signs and symptoms of illness and pain for months and months...