There are several ways to approach this situation. The most efficient way would be to see a psychotherapist, specifically an expert in treating anxiety disorders. A few sessions may be all you need to eliminate this problem from your life.
If counseling is not an option for you, then there are other possibilities. Psychiatric medication can help reduce the anxiety you feel when in public places. Perhaps your primary care physician or a psychiatrist could prescribe a medication to help you deal with this specific problem. Many people report that taking an antidepressant medication or anti-anxiety medication helps them in situations similar to yours. Some only need the medication temporarily. That may be the case with you.
Forcing yourself to engage in the behaviors you are most frightened of is often the best method for overcoming fear. Confronting your fear may be the most challenging method but often the most effective.
Hyper-intention may be at work in this situation. Hyper-intention essentially means that the intense focus on your fear makes it worse. It almost becomes a self-fulfilling prophecy. The more “life” you give the fear the more it may intensify. The solution may be to do the opposite of what you would normally do in fearful situations. You could also shift your focus. Reading doesn’t seem to be working.
A cognitive approach to this problem would be to analyze your thinking to determine if your thought process is logical. In this situation, you believe and are fully convinced that others are watching you. If we are exploring your belief from a purely logical perspective, a question comes to mind: What would prompt random people to watch you?
In addition, part of the cognitive approach is looking for evidence to prove that your belief is correct. It is important to keep in mind that just because someone believes something to be true does not mean that it is. My presumption is that there is no evidence to support your belief that others are watching you. That would make it an unsubstantiated fear. If that is the case, then you must not allow yourself to believe in any idea that is neither logical nor supported by evidence.
If this problem persists, you may want to consult a therapist. Check the find help tab at the top of this page for assistance. You may also benefit from reading self-help books including those written by David Burns. Many individuals have found that his books are particularly helpful. I hope this helps. Please take care.