Yes, it anxiety can affect you in the way you describe with heart palpitations, etc. My heart races at an anxious moment. That's why it is so important to treat it because stress and anxiety are risk factors for heart disease.
However, yours started with a new medication. This means you should check in with your doctor about it. Some medications briefly increase anxiety as your body gets used to it but you also want to make sure it isn't a direct ongoing side effect that would be dangerous or harmful to you. So, call your prescribing doctor and inform them about this for guidance. good luck
Anxiety affects different people differently. More people think anxiety affects their heart rate and blood pressure than it actually does, and no amount of negative tests can convince them otherwise. It has never affected my blood pressure and I've had an anxiety disorder for a very long time. Some of your symptoms might be nutritional deficiencies, such as a lack of electrolytes. Drugs for anxiety and depression can affect magnesium absorption, among other things. Because of this nobody can ever know for certain if symptoms are from anxiety or from something going on physically, and if you're experiencing symptoms that are new to you it might be a good idea to get a thorough check-up. If you had just started your med, I would also suggest it might be causing these, as they are common side effects of medication, but you've been on the drug for a long time it seems. It could also signal the med has stopped working, which is probably why your doc increased the dosage, but the increased dosage could be causing these side effects. You can do an experiment by just supplementing with a reasonable dose of magnesium citrate or taureate and see if the new symptoms go down, but take the magnesium at a different time from when you take your medication. If it works, it's a side effect of the increased dosage. But it could also very well be symptom of your increased anxiety, as anxiety can cause them, too.