The fact that you have these chest pains immediately followed by a pressure in your head and your bulging veins should be reason for concern.
IMO, if you already haven't, I would immediately go to a cardiologist and neurologist and have an EKG, EEG, MRI or CT-scan, carotid artery ultrasound, stress echocardiogram and whatever else they do.
Anxiety and panic can do weird things, but they're usually psychologically based or hyper-adrenal based (fight or flight). What you describe sounds very serious.
Please let us know what you find out.