First, no worries about being wordy, she is showing some odd signs.
Now I would note that Mina's reluctance to go far is quite normal in cats that feel unwell. This and hiding tend to be instinctual for our prey species, since going out into the world when you cannot pretend that you feel 100% does make you a target for predation. So, this isn't an uncharacteristic behavior for a cat that feels unwell and very unsurprising if there is perhaps another cat visiting that could be making her feel threatened. And that side of things should settle if we address the underlying issue for her.
Now the reason I noted that her signs are odd is because the do not easily fit together. We often see the gagging with nausea, but nauseous cats do not often eat more as she is. As well, we can also see the gagging signs associated with throat irritation, inflammation, dilation (megaesophagus) or damage (if she has eaten something abrasive); but again this usually does not trigger increased appetite. That said, on rare occasion we can see some animals eat or drink as a means to try to soothe the throat (just as you or I would have ice cream with a sore throat) so that would be a consideration. Furthermore, if we consider this from the other side, we can see increased appetite with issues like parasites (worms), metabolic disease (ie diabetes, thyroid issues), or organ issues (ie pancreatic disease, diseases affecting stomach acid secretion, etc). And if she was eating more and thus stretching her stomach, that could cause retching/gagging for her.
So these would be our considerations for her signs. In regards ***** ***** to address throat irritation, you could consider a trial on soft foods +/- using a cat safe cough syrup (ie glycerin/honey cough syrup with no drugs in it or even plain honey) to see if soothing her throat reduces her signs. As well, just since she is younger and worms are so commonly a cause of increased appetite, you may want to treat for those as well at this stage. And if you suspect any nausea at all, you could consider a trial on an antacid for her (ie Pepcid (More Info/Dose Here), Tagamet (More Info/Dose Here), or Zantac (More Info/Dose Here).). And further to all this, if you did want to just rule out diabetes right off the bat, I would note that you can collect (by keeping her with an empty litter box over night) a urine sample and submit that for checking before she sees her vet.
Of course, if you try this but her signs aren't settling or her appetite is severely elevated, then we'd want to consider a check with her vet. They can examine her to rule out those throat based issues +/- check bloods to rule out metabolic disease. Depending on their findings, it may just be a case of treating inflammation with cat safe anti-inflammatories) or further testing (ie ultrasound) to make sure all is well with the stomach and pancreas.
Please take care,