Thank you for your question and sorry to hear about your itchy girl Phoebe! It definitely sounds as though she is quite itchy and uncomfortable at the moment and given her patchy hair loss, it is very possible she has an underlying allergy.
First and foremost, you need to make sure that Phoebe is definitely up to date with flea control. Make sure you are using a flea product appropriate for her weight. Even if you cannot see any fleas or flea dirt on you girl, doesn't necessarily mean there are one or two lurking and oftentimes this is all it takes for a cat with flea allergy dermatitis.
Flea allergies are avoided by strict flea control - every 3 - 4 weeks with Advantage or Advantage Multi or every 5 - 6 weeks with Frontline. Do make sure you use one of these premium products as other products tend not to work very well. You must also ensure all pets in the household are treated at the same time. You should also consider flea bombing the entire house to kill all larvae and eggs hiding in your carpet.
As above, it is definitely possible Phoebe may have skin mites or lice as they commonly irritation that can lead to fur chewing like this. These could be either Demodex (less itchy) or Sarcoptes mites (VERY itchy) and you should ensure a full Veterinary skin scrape to check for mites and lice, as well as signs of fleas. There could well be something else going on here such as Demodectic mange which is a little harder to spot and requires on going treatment.
Finally cats can become allergic to many natural ingredients in their diet. I would also recommend a food trial for your girl using a hypoallergenic food like Hill's Z/D ultra available from your Vet. Feeding ONLY this for 3 weeks will give you an idea of whether a food allergy is to blame here.
Treating the allergy will treat the behavior of her scratching, licking and nibbling. If she is quite bad at the moment however, you may need to get Phoebe an elizabethan collar to discourage her. Also ensure there are no stressors for her at home as cats will sometimes start this behavior due to stress. You may even want to try the feline pheromone diffuser - 'Feliway' - www.feliway.com
Best of luck with Phoebe and I hope this has been of help to you. Please reply if you need any more information on this.
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Dr M D Edwards