A cold sore on the lip can make you extremely self-conscious and as a therapist I find that people tell me how they've called in sick to work, skipped classes or canceled meetings to avoid people seeing the lip cold sore. I do not think this is a healthy thing to do because it is a natural response to the situation. One feels helpless, judged by others and that they stick out.
Perspective is important. Everyone gets pimples, bad hair days and other cosmetic moments that are embarrassing. Let people see that you are bigger than the sore on your lip and that you will not let it dominate your day. You are much more than that. If you are expected to have a presentation at work, go ahead and give it. You will be showing your inner strength and character. People see when someone can ignore a physical problem and actually feel respect for them. It also helps you cultivate the capacity to transcend pain and itching when you do not give in to the urge to hide out.
If you are a student, you can feel that everyone is watching at you. Remember that most people are in their own worlds, thinking about whether or not someone likes them, if they can complete the homework assignment or why someone was mean to them. People tend to be a bit ego oriented and do not notice every imperfection in others. Of course, if your friends are critical and mocking then you need to evaluate if they are good for you and if the relationships are healthy. Sometimes making fun of yourself a bit can also cut through the whole situation. I had a client with a big cold sore on her lip tell me that she was very embarrassed for two days but then just let go and was incredibly relaxed around her friends. She actually found herself making jokes and being funnier than she had been in months. When we let go of things we become light and people like to be around us.
Of course, it's important to find ways to reduce the cold sores and treat them so that your immune system holds strong and you also will not spread the virus. But do not hide out. Instead let people see your personality inside and get to know the inner you.