I have curly frizzy hair but I don't straighten it. I find 3 things helpful in keeping frizz away. 1. don't blowdry (of course if you want to straighten your hair that may be hard...) 2. use a good product after washing to help weigh down your hair. I use an organic leave in conditioner that is like a thick cream. 3. Wash less. Frizzy hair actually needs oil. So I was told by hairdressers to wash my hair once weekly. Once I started doing that, my hair texture improved greatly.

Having said all of that, I don't blow dry or straighten, so I can't help much with that side of things.
Very good advice there. Does your hair have a natural curl (albeit a frizzy one)? And do you want to wear your hair curly, or dead set on straight? I find that nturally curly/frizzy hair doesn't really need the shampoo (common misconception that not usig shampoo makes your hair 'dirty'). I stopped shampooing my hair a while back and stuck only to a conditioner and a deep conditioning treatment, and my hair has never been softer/less frizzy/more managable. I still give it a good scrub in the shower, but only use the conditioner. I wear my hair curly after years of attempting to keep it straight, it looks fantastic, although you could just use conditoner and straighen, it just makes our hair type so much healthier iykwim?

Straight:

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Curly:

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I loveeeeee the curls so much more! Good luck