Regarding emotions: I forget if this is something explicitly covered in one of Ayn Rand's non-fiction books or something I cobbled together on my own, but...

Emotions are essentially hardwired reflexes. Certain input (external stimuli, maybe just internal thoughts) triggers those reflexes, which causes emotions and then causes a cascade of mental and physiological effects (fight/flight response, panic attack, depression, etc.).

Those hardwired paths can be changed, with effort. You can get over your irrational fears. You can learn psychological techniques to control your panic attacks. You can deal with your own mental issues and improve your anger issues. Ultimately, you can use reason to make your emotions more useful to you.

But emotions are not a substitute for reason or reality. Your emotional response to a situation could be totally irrational and inappropriate.

So there is a problem if you're acting solely on emotions without any basis on reality or reason. If your actions only impact yourself, then that's a bad thing for you but ultimately within your rights. It becomes a problem when people project their emotions onto the decisions of other people, which has become commonplace: "You offended me, therefore you need to be punished." That implies that emotions are valid realities, regardless of how reasonable those emotions/realities actually are.