What could cause a fast heart beat followed by dizziness in a 40 yo woman?

Low blood pressure. If the rhythm is fast enough, the heart doesn't have time to fill adequately during each cardiac cycle causing the BP to fall with dizziness and, if prolonged or severe, passing out. For this to happen, the hr is generally >170 although it depends on your age and general condition.

Related Questions

Why did I get dizzy, shakey, and a fast heart beat all of a sudden?

Many possibilities. But low blood sugar comes to mind. Trauma, emotional upset, dehydration, fever spike, acute pain e.G a kidney stone or gout attack, are other examples or possible explanations.

Today I took an infusion for hypotension. I went to emergency with dizziness, fever, fast heart beat. Please tell me how to prevent this in the future?

Dehydration. It sounds as though you were dehydrated. Were you recently ill with a decreased oral intake? Vomiting? Diarrhoea? The fever also may have caused you to lose fluid. The way to reduce the chance of this in a future similar situation is to make a conscious effort to drink extra liquids. Plain water and sports drinks are ok. Rehydration solutions are also good. Avoid sugary and caffeinated liquids.

Today I had shortness of breathing dizziness fast heart beat when I checked my blood pressure it was 160/90 its couse of panic attack or high blood pr?

Need to be seen. You are describing symptoms that could be a panic attack, but also could be a result of serious illness. Please see a physician as soon as possible to decide what is causing your symptoms.
See MD. Check with your physician to see whats going on and why you are so anxious.

I'm getting eye hem/bleed along with dizzy spells every two weeks coupled with fast heart beat. It always comes with those symptoms. Related?

Maybe. Dizziness could certainly be related to rapid heart beat. Can't relate the eye symptoms though. I see you've had an echo, EKG, and chest CT - ask your doctor for an event monitor: 24 hour, 48 hour, or 30 days - depending on how often you get your symptoms to try to catch the rhythm when you're having symptoms.

Last night I woke up out of no where half asleep so dizzy, confused, thirsty & fast heart beat. I have no idea why it happened but it was awful.

Night terror? Sounds like you may have experienced a severe autonomic response (sometimes also sweating) associated with something called night terrors. Discussion of these is well represented on the internet. Low blood sugar could also cause symptoms like this, consult your PCP.