Normal heat straightening with an iron at home is completely safe. But chemical straightening treatments like smoothening should be avoided because those chemicals can absorb through the scalp. Better to wait until after delivery.
If you mean flat-ironing with a hair straightener, go for it! But if you mean chemical straightening like keratin, please avoid it unless you want your baby to inhale those strong chemical fumes, haha. Keep it natural for a few months!
My gynac said that permanent chemical straightening contains formaldehyde and other harsh chemicals which are not safe to inhale during pregnancy. Heat flat-ironing at home is totally fine, but avoid salon chemical treatments to be safe.
Please avoid chemical hair treatments. The smell of those strong chemicals will definitely trigger horrible vomiting and nausea, trust me. Just use a normal straightener at home if you really need to.
Avoid salon chemical straightening now, it's expensive and not safe for the baby anyway. You can easily do simple blow-drying or flat-ironing at home for free if you have an event. Save that salon money for your baby shopping!