Thank you for your question.
Always consult with your doctor about any diet change.
Yes, I believe that the Atkin's Diet is generally safe for most people and is safe for people on high blood pressure medications, high cholesterol medications, and thyroid medication.
The medications you are taking do not interfere with the ketones that are formed from a high protein diet.
I have seen many patients on high protein, low carbohydrate diets have great success with blood pressure and high cholesterol.
Good Luck in all that you do with your health.