I think the Look Around Technique is used for a number of reasons. The reason is not to prove that people are never looking at us. That would be unrealistic because people do look around. People like to look at other people. There is a good reason to look at other people - maybe we are comfortable and just want to see fellow humans. Maybe we like to people watch, to look at fashion, to look at an attractive person. There are plenty of good reasons to look at someone, positive rational reasons. We don't live in a world where people never look at other people, and, quite frankly, I enjoy looking at other people - a smile, a hello, to enjoy life.
In the depths of social anxiety, I think we have the tendency to be frozen, to put on blinders, and to not ever pick our heads up to look around. We could then, possibly, create this scenario in our heads that something crazy is going on, that people are feeling a certain way towards us or that people are negative towards us. So, we break that irrationality by looking around, loosening up, checking the scene around us for rational feedback that, in fact, people might be looking at you, but often they aren't looking at you in the way you might think. And, truly, most often people are NOT looking at you very long, or just in passing. All of this feedback we get from the Look Around Technique. All of this should help to cut down on perceived anxiety and to fill out a more rational assessment of what is actually going on around you. Sometimes that rational assessment is the fact that people are indeed looking at you, but they are doing so in a kind way. And even if someone is looking at you with lack of expression, it does us no good to guess what their thought is. Their thought may range from nothing, to mild interest, to attraction. It's less likely that their thoughts would be anger or criticism. Why do I say this? Because this is what we think when we look at other people - we don't think too much about it, or we look because we have a genuine, rather positive or inquisitive perspective on what we are looking at.
How can you deal with people looking at you? Be rational. Calm down, slow down, remind yourself of the rational explanation, the most likely explanation to all this, and work to be fine in that moment. Tell yourself a rational statement which is very likely to be the most logical explanation, even if you don't feel that, tell yourself that. Break up the automatic negative assumption. There is no problem when people look at me. I don't need to worry about that. It's normal. I look at other people, too.