Well, yes, it is possible to have bloodshot eyes when you get insomnia. According to some researches, if you have insomnia, you may have bloodshot eyes, dark circles under your eyes, look pale. Also, it can lead many other diseases on your body, such as high blood pressure, heart attack. So just be careful when you get it. Maybe you need to go and see a doctor so that he can give you the exam, and medical cares. Also, you should know that bloodshot can be because of the lack of sleep and the stress. So having a rest is a good way. put some ice on your eyes, it will relieve the symptom. also, the eye drop is effective.