Can you have dizziness and feel like you will pass out being on beta blocker? Plus I feel sick in the stomach should I stop taking the medicine?

Yes. Beta blockers can lower blood pressure and heart rate. Dizziness and faintness may be a sign of these. Nausea is often one of the symptoms of near fainting as well. Let your doctor know about these and might be good to have a blood pressure cuff at home to track your blood pressure and heart rate during these symptoms.
Yes. A beta blocker is a drug that lowers blood pressure and decreases heart rate. Therefore, it can reduce blood flow to the brain and cause lightheadedness and a feeling of fainting. Check with your pmd or a cardiologist to make sure that the dose of the drug is appropriate for your problem.