Do panic attacks cause pulmonary hypertension? Or could pulmonary hypertension cause panic attacks?

No and yes. Panic attacks, while frightening cannot cause any disease themselves. Pulmonary hypertension is a chronic heart/lung disease which develops over years. Any disease process which causes shortness of breath can trigger panic attacks in people who are prone. Panic attacks are an inappropriate triggering of the system which helps us recognize when we are in danger, so shortness of breath can trip it.
Yes for second . Panic attacks not known to cause phtn whereas patients with phtn can have panic attacks due to breathing problems.
Don't panic. Panic attacks don't cause pulmonary hypertension. I'm not aware of panic attacks being caused by pulmonary hypertension, but if it was severe enough it can cause shortness of breath which could make someone anxious.