Will this hurt my cat with allergies?

My cat seems to be allergic to either (walmart) flea medicine, or fleas themselves, and has lost a lot of hair and has been acting strange lately. I recently got something called "natures guardian natural flea & tick squeeze-on for cats & kittens"

apparently, it's from all natural ingredients(Active ingredients: pepperment oil, clove oil, lemon grass oil. Other ingredients: canola oil, vanillin, citric acid)

but, it also has emergency and first aid information, things like "wash hands after handling pet, don't let pet lick it"

Any thoughts on if this will harm my cat?

I wouldn't apply anything to my cat that warns you against their licking it. OMG! Stop using that immediately! Cats have as many allergies as we do, and you might be seeing the stress of something you haven't considered yet. I suggest you drop the products from general retailers and purchase something directly from a veterinarian. I have recently found out that some of the most widely used flea medications are actually subject to counterfeiting but veterinarians are required to purchase directly from the manufacturer.A vet will recognize if your cat has a flea infestation and recommend a course of action that could include fogging your home against the eggs and baby fleas. Also to be considered: sensitivity to chemicals used in the home, such as laundry detergent and a variety of cleansers and other products.

If this just recently started to happen, it's likely that it's the medicine itself, and that your cat has been ingesting the medicine. When your cat bathes, it's probable that it's licked some of the medicine.
If your cat starts barfing, it's the medicine.
It will harm it although it won't be anything major most likely.
It's still a good idea to ask a veterinarian.