Yes, blephariti can cause bloodshot eyes in some degree. First, you should know the reason which causes blephariti. As we know that blephariti is often caused by the irritants. When your eyes are invaded by the bacteria and the irritants, it can lead to eye infection. And in some cases, it can result in blephariti. At that moment, it can make your eyes look red, and sometimes, it can lead to bloodshot eyes. And anyway, you should be careful about it. For your situation, you can put a damp, warm washcloth held over the infected eye a few times a day. In this way, it can help relieve swelling, itching and redness. Avoiding wearing contacts and eye makeup can be effective too. anyway, just pay more attention to your eyes.