My cat's fungal infection won't heal. Can I shave or bathe her?

Unfortunately, there isn't much you can do from home, especially if medications aren't helping. I would seek out another exam in person and have the vet take a scraping of the fungal site to send to a lab for testing. This can help determine what exactly it is and the best medication to put on it to help. Medicated shampoos and oral medications can also be helpful and may need a few courses to fully resolve the issue.

I would definitely keep the affected area cleaned and trimmed/clipped so you can monitor spread and more easily get medications on the affected area. Since that spot in the photo also looks like it may be infected with bacteria (abscessed) in addition, oral antibiotics from your vet is probably another good idea.

Until you can get to the vet (which I recommend doing ASAP), keeping the area clean and dry, and keeping Zuzu from scratching at or rubbing it with an Elizabethan (cone) collar (if it doesn't rub on the spot) is best. Since fungal infections can be spread to other pets and people, washing hands, bedding, clothing, etc is also a good idea to reduce spread.