The permanent makeup should not make a huge difference in your eyelids unless there is some type of infection after Asian Blepharoplasty (Dr Young Bellevue Wash). An infection would be more likely if there is more tenderness, redness, and swelling than before. You should get some swelling from eyebrow tatooing and this should be expected. Nine days is a little early to do something like that in my opinion. The reason is that after a procedure you will have swelling that is normal. Sometimes the swelling, can break down the skin defenses so it is not a good idea the more closer you do it from your surgery date. I think waiting at least 2 weeks, and to be conservative at least a month from your procedure is the more prudent thing. This is what I would have recommended to you. I would have your doctor examine the area to make sure that there is no signs of infection that would need treatment. Otherwise, I think that you should be okay and that your double eyelid operation should not suffer significant untoward effects. We also have a video demonstrating these procedures for you to see.
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Dr Young
Dr Young specializes in Facial Plastic and Reconstructive Surgery and is located in Bellevue near Seattle, Washington