A lot of what you describe, given your heart & BP being checked out, could be explained by stress and anxiety. Panic from stress, great fatigue can happen from stress, feeling light headed can happen with stress, and muscular tension headaches or even migraines can be triggered with stress.
But if you haven't gotten them checked out, you should make an appt. with your primary care doctor and ask for a ferritin test, to make sure you aren't suffering from low iron, which can cause fatigue, dizzy feelings and rapid heart rate & thryoid function testing- to make sure you don't have hyperthyroidism.
You also need to be take steps in dealing with trying to prevent these panic attacks with some stress management. If you are a Christian, casting your cares on the Lord is a big part & reading from or listening to God's Word. Listening to soothing music and doing some deep breathing can be helpful. Distracting yourself with an activity you enjoy also can be of help. And for occasional use, if necessary, you might see a psychiatrist about some low dose tranquilizers for those panic attacks you don't manage to stave off.
You should get a second opinion. If you do not feel that this is anxiety, then do not accept the diagnosis and find another doctor. Its possible that it is is anxiety and if your neurologist thought that was the diagnosis, they should have prescribed you anti-anxiety medicine or relaxation techniques. If I were you, I would seek a second opinion.