No, there is no reason why you can't be under a hair dryer. It's perfectly safe. Looks like your baby is a really active one and he was just waking up because you weren't rocking him to sleep by your movement.
Hot showers increase your body temperature and can cause problems with the baby's brain development. It is easier to have your body temperature up to an uncomfortable level when it is wet than when it is dry heat...imagine what it would be like taking a walk in 120 degrees like the temperature people take their showers in. You just couldn't do that.
If you yourself were feeling too warm or uncomfortable under the dryer, then that would mean your are too hot. Just trust your own reflexes.
The main thing I'd be worried about more than the heat here is the chemical treatment that you might have had. It's recommended to stay out of salons for treatments during pregnancy. There isn't enough evidence that it does actually harm the baby, but most stylist won't accept pregnant moms for hair treatments until after the baby is born.