I had a bike accident that caused facial laceration a few millimeters away from my right eyes, on the eyelid. The doctor applied 7 stiches and said that I should not touch it or put water on it for at least 24-48 hours, and avoid putting too much water for 5-10 days. Can I do tayammum in this case?

You can make wudhu and avoid the area or your face if the doctor says so, so do what you are able to do only according to the doctor's advice. Some of the ulama mentioned that u do wudhu then u do tayammum for whatever is missing, but i didn't find any evidence for this due to my ignorance and Allah knows best.