My two year old daughter has LI and she has had two surgeries so far to correct her drooping right eyelid. She was diagnosed at 4 months with a condition called ptosis. This is the result of ill-formed muscles that hold the eyelid open. In her surgeries, the ped. opthamologist used rubber tubing to connect her eyelid to the muscle that lifts your eyebrows and that is the muscle that now opens and closes her eyelid.
I know that sounds really involved and scary, but it's really not that bad and if you look at her now, you can't even tell she's had surgery. We've been warned that it doesn't necessarily last forever and she will likely have at least one, if not more surgeries to continue to replace it, but it's old hat to us at this point, so I'm not concerned. Our opthamologist generally waits until the child is 4 or 5 to do the surgery, but Cate's eyelid was drooping enough that it was obstructing her view and he was afraid she wouldn't develop properly since she couldn't see properly, so they did it early.
I hope this makes sense! If it is ptosis, don't worry - it's definitely fixable, sometimes doesn't even need to be fixed, and truly not a big deal in the grand scheme of things.
Hang in there!