1 year post and eyelid still swollen? Will this swelling heal over time or would something like a cold compress help? (photo)

There should not be any swelling after 1 year. There could be residual ptosis present but also the hollowness compounds the appearance of it.

The implants, based on the photo, seem to not have fallen into the pockets. You are already fully healed and you wouldn't expect any more changes to occur at this point in time. Revision surgery is an option. Schedule an appointment with your board certified plastic surgeon for an in-person examination.

Ptosis surgery can cause more lasting swelling due to the depth of the surgery in the eyelid. However after 1 year, any swelling you see is likely not true swelling but the result of the surgery. Issues with crease formation, partially remaining ptosis, and volume loss can all cause the appearance of swelling.