Yep, it could cause that. Bloodshot eyes or red eyes, is a harmless eye condition due to the blood vessels are too close to the surface of the eye becoming dilated and enlarged. You would not feel any pain thus you would noticed it from others or look into the mirror by yourself. One common cause of it is subconjunctival hemorrhage, in other words, the thin blood vessel bursts and appears on your eye. It may break for many reasons, including flying. Because there is higher pressure on the air than on ground, your body, your eyes also have high atmospheric pressure. Hence, it would make your blood vessels burst to cause bloodshot eyes.
When you get off the flight, the blood pressure may be suddenly raised. And the eye pressure will get increased too. That is why you get the bloodshot eyes. However, it will be ok. You should have the good rest for the eyes these days. You should not eat the spicy food these days which may stimulate your eye nerves.
Yes, it is quite possible for you to get bloodshot eyes after flying. Those may be the reasons your eyes appear red when you get off the flight.
First, the flight will cause dryness, and this kind of dryness can cause scratchy and bloodshot eyes.
Second, your body can get tired, so that your body can get dehydrated, as well as your eyes.
To avoid red eyes, just use little saline pouchs, the saline water will help maintain water in your eyes, while not sensitive to your eyes.