Sure you can. The general rule is no sharp items & liquid stuff in your handbag, but it's okay in the bag which you will check in. As for electric devises like hair curling irons and straighteners, I've never heard any rules regarding those.
The irons are allowed. Any liquids (mousse, perfume, hairspray, makeup, etc.) must be no larger than 3oz per package, they ALL must fit into a 1 quart ziploc bag, and you are allowed ONE ziploc bag per person. Everything else must be checked.
The irons are allowed. Any liquids (mousse, perfume, hairspray, makeup, etc.) must be no larger than 3oz per package, they ALL must fit into a 1 quart ziploc bag, and you are allowed ONE ziploc bag per person. Everything else must be checked.