How long should I be icing if swelling is still present after an upper and lower eyelid surgery?

Each doctor is different, I have patients use frozen peas or ice with a barrier for 20 minutes on and 20 minutes off for the first night.  Best to review with your surgeon.

You will hear many opinions on timing and technique... but this is what I tell my patients. Fill a bowl with clean water and float a few ice cubes. Use a face cloth dipped and wrung out. Fold twice to form a rectangle and place over both eyes. Dip the cloth when it becomes warm. The cloth conforms to the contours of the eyelids, providing cool wetness, and is not heavy on the eyes or lids. If you are bored, do one eye at a time and watch a good movie.
Frozen vegetables may be heavy and too cold for comfort. You don't need to have ice or frozen veggies on your eyelids - just a cool wet cloth. I have my patients use the cool compresses continuously while awake. Take breaks for food and rest room. Stop when you go to bed. Do this for 48 hours - or more if it makes you comfortable and you want to continue. After 48 hours +/-, use warm compresses in the mornings to partially remove the old ointment and any debris, dabbing lightly - don't wash or scrub! The closer my patients adhere to these instructions, the less swelling and bruising they will have when they come back to the office for followup.
The cool compresses also serve to keep patients occupied so they do not try to get back to their activities. It is important to avoid aerobic activity, lifting, bending, straining... so if you are doing compresses for 48 hours, you are not getting into trouble!
Best wishes with recovery!