Is it normal to feel dizzy a few days later after stopping caffeine and diet soda?

Very Possible: Abruptly stopping caffeine can definitely have withdrawal side effects. The most common is a headache and a lot of people who drink coffee at work get "weekend headaches" when they don't drink as much caffeine at home. To some degree it depends on what you mean by dizzy. Lightheaded type dizziness would be expected as would a headache. A sensation of true spinning is different and not expected.