I am sorry about your sisters ailment. I wish you luck with a doctor!
Hi,
Maintaining body balance is a function of the cerebellum which is an integral part of the brain. Also issues with the middle and inner ear can cause your sister to lose balance. Head wobbling or giddiness or feeling fuzzy can be due to low blood pressure, anaemia, ear problems and central nervous system problems. Hence you should take the opinion of a neurologist and a ENT expert.
The answer is based on information provided. Exact advice is not possible without a proper examination and investigations. You are requested to consult your Doctor. Take care and keep us posted.