Sometimes your eyes can simply just get dried out due to not enough moisture in your eyes which you can remedy by adding some moisturizing eye drops to your eyes.
If the red eyes are not caused by dried eyes and aren't just irritated then yes the red eyes could be caused by high blood pressure.
When your blood pressure gets high it can lead to blood vessels in your eye popping which can cause red eyes, blurry vision and sometimes even a complete loss of vision.
The broken blood vessels in your eyes is also known as a subconjunctival hemorrhage which often occurs without any obvious harm to your eyes and it usually remedies itself without any treatment.
But if your vision gets worse or the blood doesn't go away within a few days to a week then you might want to go to the emergency room, urgent care or your eye doctor.