Should a woman continue her fast despite suffering from diabetes and experiencing pain such as dizziness, headaches, and difficulty moving?

There is no blame upon you for delaying the make-up fasts if you are a diabetic unable to fast, until Allah cures you and you are able to make them up, even if it is after another Ramadan (definition). This is based on the Almighty's saying: "Allah intends for you ease and does not intend for you hardship," and His saying: "Allah does not burden a soul beyond its capacity." You are only required to make up the fasts. It is advisable to consult a specialized doctor to determine the possibility of fasting or not.