Insulin dependency does not preclude you from teaching in China. The only lab results that do disqualify one for employment as a foreign teacher in China are those that are positive for HIV and other contagious illnesses. Diabetes is not contagious, so it does not directly affect your physical suitability for employment. Barring the presence of STDs, it is very difficult to fail the Physical Exam Record for Foreigners in China.
Insulin and syringes can be purchased at any hospital in China as well as at large pharmacy chains. In some provinces and cities, you won't even need a doctor's prescription--although I would strongly advise you to find and consult with a competent or Western-trained Chinese doctor in your area to begin with. Some drug manufacturers will be more reliable than others and a Chinese physician will know this information. The total cost will be a fraction of what you are paying now.
You didn't mention if you will be working for a public or private school. The position of the vast majority of public schools will be that if you can pass the physical, then that's all they care about. Regarding private schools, just as long as you don't impose any scheduling restrictions on the owner, he or she shouldn't care as well. Diabetes, like hypertension, is not stigmatized in China (unlike, for example, mental health issues).
Good luck to you!