These do sound more like typical PMS things than pregnancy-related symptoms. Usually, early signs of pregnancy will include food aversions although getting lightheaded and even sweaty from the shift in hormones isn’t unheard of.
The odds of getting pregnant on the Depo shot are only about every 3 in 1,000 women using it correctly - those are slim chances.
Some women will continue to have periods even after receiving the injection, and that could explain why you’re feeling so off right now. If I were you, I would take a test in a few days just to make sure. If the test is negative and the icky feelings continue, call your primary doctor or whoever administered the birth control and just let them know what’s going on. It may be usual side effects, a virus or something that needs treatment so you can get back to your old self!