Is it normal for a blue nose pit to have bloodshot eyes?

No, it is not normal. Your dog might be having an allergic reaction to something. It could be anything, food, treats, medicine, summer allergies, and so on. Your best bet is to take your blue to the vet to make sure. Remember, Blues are more prone to allergies, skin rashes, among other things. They are the most delicate of the pitbull world. Good luck, hope your Blue doesn't have anything serious.