Well, generally speaking, it is normal to have bloodshot eyes after you have taken the nose surgery, for your eyes can be affected by your nose. And you may know that bloodshot eyes can be caused by irritation, allergies, eyestrain, environment, wearing contact lenses, dry eyes. So when your nose is infected, it can affect your eyes, and then lead to red and bloodshot eyes. For your situation, you can use some cold ice with the compresses will be effective too. Also, some eye drops are essential too. Or you can just go and see the eye doctor.
Well, you should know that there will be some side effects after taking nose surgery, so this is one of the consequences. But you could relieve because the bloodshot eyes are just temporary and could go away if you get some eye drops under the doctor's directions, maybe they look very awful but no victory comes out without price. Just consult the doctor .