Is there a way to correct my asymmetry of eyelids without surgery? One droops/

Few. If you are an eyeglass wearer, there is an extension on the back of eyeglasses that an optical shop can make called ptosis crutch which will elevate one eye. It is slightly annoying to use but you can get used to it. Otherwise you will have to correct your ptosis with surgery that is minimally invasive, not painful and can be recommended by your oculoplastic surgeon.
Ptosis crutch. A drooping eye lid is called ptosis. If this is of recent onset, the first thing you should do is visit your eye doctor to determine the cause. Once you know the cause you will know if this will be stable. If it is stable, the options are surgery or an attachment to glasses called a ptosis crutch which some opticians can fit.