Hair straightening iron should be okay, assuming it's the normal plug-in kind that is similar in size to a curling iron?
Makeup is trickier, it has to be smaller than 100ml if liquid. Powders are not an issue regardless of size. If you have liquid or gel stuff (foundation, moisturizer, eye serum, acne meds, liquid eyeliner, anything like that - or any hair products like gel, shampoo, conditioner, or hairspray) they have to be in containers 100ml or smaller, and ALL of the little containers must be packed in a small (20cm x 20cm) ziploc bag. Each person is allowed one of the bags of liquid containers in their carryon.
For packing this type of thing in your checked bags, there is no restriction with size or amount. You can pack full-size bottles of shampoo, etc in checked luggage.
HTH!