Feelings of nausea and headaches could be hunger/low energy. Also, in case you’ve not been advised already, be careful with calorie deficit and breastfeeding. Apparently breastfeeding burns an average of 500 calories and too much of a deficit could impact your supply and effect babies growth.
I used to feel that way whenever I went more than a few hours without eating. Once I stopped breastfeeding, it went away. If you plan to breastfeed for a while, you might want to hold off on strict IF until then. I managed to lose a lot of weight doing low carb (not keto, more like under 50 carb) while breastfeeding and stayed pretty comfortable. It’s really hard to deal with little ones and a headache at the same time.