You have upper eyelid retraction. The most common cause to this is thyroid related orbital disease. Your internist can test your thyroid function. The eyelids should be assessed by a fellowship trained oculoplastic surgeon. They can also discuss with you how this is managed. I also have...
The asymmetric eye appearance is likely due to multiple factors including bony asymmetry, eyelid asymmetry, and eyeball position asymmetry. Best to see an oculoplastic specialist for evaluation. See following video too.