If you should carry on, with what? Fasting?
Nausea, dizziness and headache could be caused by having too low blood sugar, which could be a result of fasting, particularly, if you have any type of blood sugar disorder, such as diabetes or hypoglycemia.
Your belief will determine whether or not you must continue fasting.
I have heard within Islam it is advisable that a person not fast if they have a medical issue which means they cant.
It isn't a sign of spiritual weakness, you just cannot do it.