When Can I Start "Washing my Eyes" After Double Eyelid Surgery?

This is an excellent question to ask your surgeon and not others who did not perform the surgery. Your surgeon may have used certain techniques and have a specific protocol in place which they feel is essential to an excellent outcome.

Every surgeon should be meticulous about the way they operate and how their postoperative instructions are communicated because successful outcomes depend on it so you should specifically ask your surgeon. Every surgeon I know do slightly/completely do different thing yet most get good results. 
Things that are reasonable after eyelid surgery are 
- Keeping it dry for a couple of days
- Using gentle irrigation with some normal saline to get rid of crud and dabbing it dry
- Using some eye lube to keep it moist especially at night
- Some ice packs to reduce swelling in the first couple of days 
- Avoid make up until further advice, I usually don't like it on it for a couple of weeks at least.
Wish you the best in your journey.
Dr Leo Kim, Specialist Plastic Surgeon

The best advice I can give is that you should follow the postoperative instructions given to you by your Surgeon and no-one else.  A well trained, well organized Surgeon should have specific instructions (typically in written form) outlining the do's and don'ts after surgery.