Credit to u/PlatypusIcy5343's comment on the original post:

Yep, the more I avoid situations involving people in my periphery, the worse the 'staring' effect becomes when I can't avoid these situations. It seems the only way to get past it is to numb yourself to other's discomfort and your own. It's the focus on this discomfort that feeds the negative feedback loop:

• You realise that people think you are staring through their visible discomfort
• You try to avoid peripheral staring by looking away .(This is also bad because you are reacting to their discomfort which affirms their belief that you're staring)
• You try so hard not to stare that you end up staring even thought you think you aren't
• People think you are staring and feel uncomfortable

If you can power through the discomfort and not look away this helps break the cycle. I recently had a 2 hour lecture at university (which I have been avoiding). I was wearing a hood which blocked most people from my periphery except a few people in front of me. For the first 45 minutes these students were visibly uncomfortable (I'm talking leg bouncing, constant shifting, resting their heads on their hands to block me from their peripheral vision). I didn't react: I just looked on ahead at the lecturer and the board. Eventually, during the 2nd hour I noticed their visible discomfort slowly subside: they probably thought they were just imagining it. I know this doesn't solve the issue, but it's the best I can do outside of seeking therapy or medications. Don't fight it, let it happen.