If you're against surgery at all costs, laser will tighten the skin for some time and is easy to do and recover from. Otherwise manually elevate your brow and if its not giving you the deer in the headlight look and you like how your lids are better creased and your eyes more alert looking, ...
There are several options. Leave invasive and most predictable would be filler injection in upper eyelids. Fat injection is another option but less predictable. Another more invasive option would be orbital implant to push the eyeball forward but doubt that is what you need. Consultation necessary.
From the picture you posted it appears both lower eyelids are pulling down although the right one is worse. I would definitely use artificial tears during the day and sustained ophthalmic ointment at night to help with the irritation. At this point since it is not severe I would hold off on...
