Would a sinus infection/upper respiratory infection/ antibiotics / cause random spike in blood pressure and or high 90's heart rate?

Possibly: Any time your body is under stress, including when you are sick, your vital signs can be affected, including your blood pressure and heart rate. But don't ignore these, either. When you're feeling better, make sure to have them rechecked to see they return to normal. If not, then you need to consider other causes. If your blood pressure is dangerously high, seek cause sooner rather than later!