Well, I can see that you are worried about your eyes. So, it is true that sometimes hay fever could give rise to a lot of problems and symptoms, including allergic rhinitis ,which is quite serious and could lead to red eyes and allergic conjunctivitis. I myself used to get that and I suffered a lot from it. Anyway, you should try to avoiding exposing to flowers or allergic sources, and get some antibiotic eye drops to deal with the problem. And take more exercise could help.
Yes, it is possible for you to get eye infection because of hayfever. You may get the weak immune system which will make your eyes get the bacterium easily. You could find that the eyes become to feel uncomfortable. You could use the eye drops to release the symptom. In addition, you could use the medical treatment to cure the eyes infection.
Well, of course, yes, hayfever can lead to eye infection. As we know that when you have a cold which is caused by the virus, it is possible to have hay fever. in that way, your eye immune system can be weak, and then the virus will invade into your eyes, leading to eye infection. And at this moment, your eyes will turn to red and bloodshot, in some degree, it can be itchy too. To treat your bloodshot eyes, you should take some measures to heal your high fever. For example, you can drink hot beverages. According to some studies, a hot drink provides immediate and lasting relief of cold symptoms such as runny nose, cough, sneezing, and sore throat. And also, you should eat a diet rich in fresh fruits and vegetables. You should know that these foods provide lots of antioxidants, which may help boost your immune system, especially vitamins A and C. in this way, I think it can do a help to your eyes.