Yes they all can be yeast symptoms. especailly if you had thrush and vaginal itching. Even if it's gone now, candida is hard to wipe out if it's systemic.
We also have yeast/eczema/diaper rash issues.
Low-carb won't hurt. What is important is getting enough saturated fat. Coconut oil will be very helpful (2 -3tbs/day) for both of you. You cannot take harsh treatments like oregano oil, so your choices are garlic, coconut oil and Nystatin. And low-carb. And lots of probiotics, digestive enzymes. Check out the healing the gut tribe sticky candida/yeast section for advice...
You can also try taking yeast-killer enzymes like candex or candidase. It gave my bf DD a rashy die-off reaction, though.
Ketosis is not harmful if you're not a diabetic. However, I don't think you'll go that far if you eat plenty of veggies and moderate amounts of nuts. By low carb I mean no sugar (any form) and grains, very little low-sugar fruit such as berries.