The typical amoxicillin dosage for cats is 5 to 10 mg per pound every 12 to 24 hours. However, the actual dosage for your cat would be best determined by your vet after an in person exam and definite diagnosis. If you give the lowest recommended dose, at 5 mg. per pound of body weight, and your cat weighs 16 lbs., this comes out to 80 mg., and I really don't think you will be able to accurately cut the 875mg. tablet into 10 equal parts. The highest dosage, at 10mg. per pound would mean cutting the tablet into 5 equal parts, also not easy, but 'easier'.
Some serious side effects of this medication can include shortness of breath, bloody diarrhea, hives, rash, fainting, swelling of the tongue, face or lips, bruising, unusual bleeding or seizures. Some less severe side effects include nausea, vomiting, abdominal pain, fungal or yeast infection.
I completely understand your financial bind, and would recommend trying your best to get your cat evaluated by a vet, and prescribed the most appropriate medication/dosage for her UTI, if this is the condition diagnosed. The organizations listed at the link below, may help you pay for vet fees and medications, if you qualify, and if you're located in the U.S.:
Also, call your Humane Society, ASPCA, and local cat rescue organizations to see if they can recommend a vet they use, one who may be lower-cost, and/or might treat your cat free of charge, considering your extenuating circumstances.
I hope all will be well with your furry girl.