Yes for the hair dryer, but the straightener ( if it is a cream or liquid) needs to be in a plastic bag and less than 3 oz. If you put it in checked bags there is no question, but you can carry it...
You could only take this product in your carry-on if it's three ounces or less by volume AND it's in a clear plastic, zip-loc style bag. Many, but not all, airports provide these plastic bags prior...
I just went traveling yesterday and I had a straightener in my bag and everything was fine. They did swab it, but just to make sure it's not a bomb or something.